Conditional Probability of 

Release (CPR) Estimates for 

Railroad Tank Cars in 

Accidents

RA 19-01 

by 

Todd Treichel 

Laura Ghosh 

M. Rapik Saat 

Christopher P.L. Barkan 

Xiang Liu 

Steven Kirkpatrick 

Junho Song 

Xiaonan Zhou 

February 2019 
RA-19-01 

February 2019 

i 

DISCLAIMER 

This report was sponsored by the industry partners of the Advanced 

Tank Car Collaborative Research Program (The American Chemistry

Council, The Association of American Railroads, The Chlorine 

Institute, The Fertilizer Institute, and The Railway Supply Institute) 

and published by the RSI-AAR Railroad Tank Car Safety Research 

and Test Project. It is disseminated for informational purposes only 

and is given to, and is accepted by, the recipient at the recipient’s sole 

risk. The sponsors, the RSI-AAR Project and the University of 

Illinois at Urbana-Champaign make no representation or warranties, 

either expressed or implied, with respect to this report or its contents. 

The sponsors, the RSI-AAR Project and the University of Illinois at 

Urbana-Champaign assume no liability to anyone for special, 

collateral, exemplary, indirect, incidental, consequential, or any other 

kind of damages resulting from the use or application of this report 

or its contents. Any attempt to apply the information contained in 

this report is made at the recipient’s own risk. 

 
RA-19-01 

February 2019 

ii 

1. REPORT NO.

 RA-19-01 

2. REPORT DATE

 February 2019 

3. PERIOD COVERED

 n/a 

4. TITLE AND SUBTITLE

 Conditional Probability of Release (CPR) Estimates for Railroad Tank Cars in Accidents 

5. AUTHOR(S)

 Todd Treichel, Laura Ghosh, M. Rapik Saat, Christopher P.L. Barkan, Xiang Liu, 

 Steven Kirkpatrick, Junho Song, Xiaonan Zhou 

6. PERFORMING ORGANIZATION 

 RailTEC 

 University of Illinois at Urbana-Champaign 

 1239B Newmark Engineering Laboratory MC-250 

 205 North Mathews Avenue 

 Urbana, IL 61801 

7. TYPE OF REPORT

 Research 

8. CONTRACT OR GRANT NO.

 n/a 

9. NO. OF REFERENCES 

 4 

10. SPONSORING AGENCY 

 RSI-AAR Railroad Tank Car Safety Research and 

 Test Project 

 13541 Taylorstown Road 

 Leesburg, VA 20176-6165 

11. NO. OF PAGES

 

 108 
RA-19-01 

February 2019 

iii 

12. ABSTRACT

This report presents estimates and formulas for conditional probabilities of release 

(CPR) for all common tank car configurations and components in service today, given 

that the tank car is involved in an FRA-reportable accident, as well as distributions of 

the quantity of lading lost in the event of a release. The study was funded by the 

industry partners of the Advanced Tank Car Collaborative Research Program, using 

data provided by the RSI-AAR Railroad Tank Car Safety Research and Test Project. 

The study updates and expands upon an earlier Tank Car Safety Project report: 

RA-05-02, “Safety Performance of Tank Cars in Accidents: Probabilities of Lading 

Loss”, published in 2006. 

The purposes of revising the RA-05-02 CPR estimates were to take advantage of data from 

more recent accidents, and to incorporate factors in the modeling of tank car performance 

that were not addressed by the earlier report. The new estimates are more reflective of 

current and future tank cars and accident environments. 

CPR estimates for the more recent time period are generally lower than the RA-05-02 

estimates for any given car. Some of the newly analyzed variables were revealed to be 

significant. 

13. SUBJECT TERMS

 Tank Cars 

 Accident Safety 

 Tank Damage 

 Hazardous Materials 

 Risk Analysis 

 Lading Loss/Releases 

 

14. AVAILABILITY STATEMENT

 Contact sponsoring organization. 
RA-19-01 

February 2019 

iv 

Conditional Probability of Release (CPR) Estimates 

for Railroad Tank Cars in Accidents 

Contents 

 Page 

Executive Summary............................ vi 

1. Objectives......................................... 

2. Approach.......................................... 

 a) Definition of “conditional probability of release”

 b) Analytical team 

 c) Data used in the study 

 d) Identification of variables for regression 

 1) Accident-related independent variables 

 2) Car-related independent variables 

 3) Variables considered but not included 

 4) Definition of estimated effective impact speed 

 5) Definition of impact opportunity factor 

 6) Advanced variable selection procedure 

 e) Regression approach 

 f) CPR for one-component losses 

 g) FRA multiplier 

 h) CPRs adjusted for minimum quantity lost 

 i) Quantity lost 

 j) Expected Quantity of Release (EQR) 

 

 1 

 

 2 

 2 

 2 

 2 

 4 

 4 

 4 

 6 

 7 

 8 

 9 

 9 

11 

12 

12 

13 

13 

3. Results............................................ 

 a) CPR formulas 

 1) Shell CPR formula 

 2) Head CPR formula 

 3) Top fittings CPR formula 

 4) Bottom fittings CPR formula 

 b) CPRs for common tank cars and other cars of interest 

 c) Tank thickness effects 

 d) Tank steel type effects 

 e) Top fittings protection effects 

 f) Jacket effects 

 g) Head protection effects 

 h) Speed effects 

 i) Yard/industrial CPRs 

 j) Quantity lost results 

 k) Expected Quantity Released (EQR) Example 

15 

15 

15 

15 

16 

16 

18 

19 

20 

21 

22 

23 

24 

27 

27 

33 
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4. References............................................ 34 

Appendix A: Tank Car Safety Project Collection of Data on Tank Cars Damaged in Accidents 

Appendix B: gMCP (Group Minimax Concave Penalty approach) 

 

Appendix C: Final Model Output, Model Fit and Diagnostics 

Appendix D: Uncertainty Surrounding CPR Estimates 

Appendix E: Calculation of the FRA Accident Data Compatibility Multiplier 

Appendix F: Comparison of TWP-17 and RA-05-02 CPR Estimates 

Tables 

 Page 

1. Number of Tank Car Records Used in Each Component Regression, and the Number 

of Accidents in which Those Cars Were Damaged 

 

 3 

2. CPRs and CPR>100s for Selected Tank Cars Under Average Mainline Derailment 

Conditions 19 

3. CPRs and CPR>100s for Selected Groups of Comparable Tank Cars with Different 

Tank Thicknesses, Under Average Mainline Derailment Conditions 20 

4. CPRs and CPR>100s for Selected Pairs of Comparable Tank Cars with Different Tank 

Steel Types, Under Average Mainline Derailment Conditions 21 

5. CPRs and CPR>100s for Comparable Tank Cars with Different Top Fittings Protection 

Levels, Under Average Mainline Derailment Conditions 22 

6. CPRs and CPR>100s for Selected Pairs of Comparable Tank Cars with and without 

Standard 11-Gauge Jackets, Under Average Mainline Derailment Conditions 23 

7. CPRs and CPR>100s for Selected Groups of Comparable Tank Cars with Different 

Levels of Head Protection, Under Average Mainline Derailment Conditions 23 

8. CPRs and CPR>100s for Selected Cars Derailed at Different Speeds, Under Otherwise 

Average Mainline Derailment Conditions 24 

9. CPRs and CPR>100s for Selected Cars Derailed on Different Track Types, Under 

Average Mainline Derailment Conditions 27 

10. Number of Tank Cars that Lost Lading, by Percent of Tank Capacity 32 
RA-19-01 

February 2019 

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12. EQRs, CPRs and CPR>100s for 30,000-Gallon DOT-111 Tank Cars with Different 

Risk Reduction Options (RROs), (7/16” Tanks, 119” Shell Inside Diameter), Under 

Average Mainline Derailment Conditions 33 

13. CPR Estimates and Associated Confidence Intervals for Five Tank Car 

Configurations 

D-2 

14. TWP-17 CPRs and RA-05-02 CPRs for Selected Tank Cars, Under Average 

Mainline Derailment Conditions 

F-1 

Figures 

 Page 

1. Effective Impact Speed (EIS) Curve for a 10-Car Derailment at 40 mph 8 

2. Impact Opportunity Factor Curve for a 15-Car Derailment 9 

3. Four Components of a Tank Car That Can Lose Lading 10 

4. Relationship Between Tank Thickness and CPR, Illustrated for Jacketed and NonJacketed 111A100W1 Tank Cars, Under Average Mainline Derailment Conditions 20 

5. Non-Jacketed 111A100W1 Mainline CPR vs. Train Speed as Predicted by TWP-17 

Formulas, and Empirical Counts 

25 

6. Jacketed 111A100W1 Mainline CPR vs. Train Speed as Predicted by TWP-17 

Formulas, and Empirical Counts 

26 

7. Average Quantity of Lading Lost for Each Car Component, Expressed as a 

Percentage of Car Capacity 

28 

8. Distribution of Percentage of Car Capacity Lost for Each Car Component 30 

9. CPRs for Five Tank Cars, with 95% Confidence Intervals D-2 
RA-19-01 

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1. Executive Summary 

 This report presents estimates and formulas for conditional probabilities of release (CPR) 

for most common tank car configurations and components in service today, given that the tank 

car is involved in an FRA-reportable accident, as well as distributions of the quantity of lading 

lost in the event of a release. The study was funded by the industry partners of the Advanced 

Tank Car Collaborative Research Program (The American Chemistry Council, The Association 

of American Railroads, The Chlorine Institute, The Fertilizer Institute, and The Railway 

Supply Institute), under the ATCCRP designation “TWP-17”. The data used in the analysis 

were provided by the RSI-AAR Railroad Tank Car Safety Research and Test Project (the Tank 

Car Safety Project). The study updates and expands upon an earlier Tank Car Safety Project 

report: RA-05-02, “Safety Performance of Tank Cars in Accidents: Probabilities of Lading 

Loss”, published in 2006. 

 The purposes of revising the RA-05-02 CPR estimates were to take advantage of data 

from more recent accidents, and to incorporate factors in the modeling of tank car performance 

that were not addressed by the analysis in RA-05-02. The new estimates are more reflective of 

current and future tank cars and accident environments. Some representative CPR estimates 

for average derailment conditions are shown in Table E1 (mainline/siding accidents). 
RA-19-01 

February 2019 

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Table E1 

CPRs and CPR>100s for Selected Tank Cars 

Under Average Mainline Derailment Conditions1

Car 

Specification 

Head and 

Shell 

Thickness 

(in.) 

Head and 

Shell Steel 

Type 

Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

Shell 

Inside 

Diameter 

(in.) 

CPR CPR>1002

111A100W1 0.4375 A516 No No No Yes 119 0.274 0.2003

111A100W1/3 0.4375 A516 Yes No No Yes 119 0.134 0.089 

111A100W1/2 0.4375 A516 No No No No 119 0.265 0.194 

111A100W1/2/3 0.4375 A516 Yes No No No 119 0.130 0.086 

111A100W2 0.5625 A516 No No Yes No 100.625 0.201 0.167 

111A100W1 0.4375 TC128B Yes Full Yes Yes 119 0.064 0.046 

111A/S100W1 0.500 TC128B No Half Yes Yes 119 0.132 0.103 

117R100W 0.4375 A516 Yes Full No4 Yes 119 0.126 0.081 

117R100W 0.4375 TC128B Yes Full Yes Yes 119 0.064 0.046 

117R100W 0.500 A516 Yes Full No4 Yes 119 0.106 0.067 

117R100W 0.500 TC128B Yes Full Yes Yes 119 0.052 0.037 

117J100W 0.5625 TC128B Yes Full Yes Yes 119 0.042 0.029 

112J340W 0.625 TC128B Yes Full Yes No 118.75 0.033 0.023 

105J300W 0.562 TC128B Yes Full Yes No 118.75 0.040 0.028 

105A500W 0.779 TC128B Yes No Yes No 102 0.040 0.030 

105J500W 0.797 TC128B Yes Full Yes No 102 0.031 0.022 

112J500I H1.03 / S0.89 TC128B Yes Full Yes No 115.34 0.017 0.011 

105J600I H1.136/S0.98 TC128B Yes Full Yes No 106 0.016 0.011 

Criteria for the inclusion of a tank car in the study’s dataset include: 

• Accident occurred 1980 through 2011, the latest year for which complete data were 

available at the time of the analysis 

• Car was built 1970 or later 

• Loaded cars only 

• Stub-sill cars with shelf couplers only 

 

1

 Assuming average conditions for a freight car in an FRA-reportable mainline accident: 29 mph train speed at the 

moment of derailment, 11 cars derailed, and the tank car of interest is the 6th derailed car. These averages are 

derived from FRA mainline and siding freight train accidents for the period 2003-2012. Note that CPR>100 is 

defined in section 2(h) of the report. 

2

 CPR adjusted to exclude releases of 100 gallons or less from an individual car. See Section 2(h). 

3

 Preliminary analyses used CPR = 0.266 and CPR>100 = 0.196 for non-jacketed DOT/TC-111 cars. Subsequently an 

adjustment was made to the tank steel assumption that resulted in a slight increase in the CPRs. 4

 Specifications for 117R100W require top fittings protection. However, while there are many different types and 

levels of top fittings protection today, the data used for this study did not allow those distinctions to be made 

quantitatively. Top fittings protection was either an impact-resistant protective housing, or none. Some current 

systems probably perform somewhere in between. Therefore, some examples using “No” for this field are presented, 

to suggest the range of performance that the real systems probably fall within. 
RA-19-01 

February 2019 

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• Tank car classes DOT/TC-111, 211, 105, 112, 114, 120 only 

• Tank steel specifications TC128B, A515, A516 only 

• Truck capacity 100 tons or more and 4 axles only 

• Damaged by impact (as opposed to strictly by fire exposure). 

This study focuses strictly on the effects of immediate impacts during a derailment. Subsequent 

effects of fire exposure, for example, are not addressed. 
RA-19-01 

February 2019 

1 

Conditional Probability of Release (CPR) Estimates 

For Railroad Tank Cars in Accidents 

1. Objectives 

 This report presents estimates and formulas for conditional probabilities of release (CPR) 

for most common tank car configurations and components in service today, given that (i.e., under 

the condition that) the tank car is involved in an FRA-reportable accident, as well as distributions 

of the quantity of lading lost in the event of a release. The study was funded by the industry 

partners of the Advanced Tank Car Collaborative Research Program (ATCCRP) (i.e., The 

American Chemistry Council, The Association of American Railroads, The Chlorine Institute, 

The Fertilizer Institute, and The Railway Supply Institute), under the ATCCRP designation 

“TWP-17” (Technical White Paper 17). The information on car features, accident details, tank 

car damage and lading loss that were used in the analysis was drawn from data that have been 

compiled since 1970 by the RSI-AAR Railroad Tank Car Safety Research and Test Project (the 

“Tank Car Safety Project”). This study updates and expands upon an earlier Tank Car Safety 

Project report: RA-05-02, “Safety Performance of Tank Cars in Accidents: Probabilities of 

Lading Loss” [Ref. 4], published in 2006. 

 The purposes of revising the RA-05-02 CPR estimates were to take advantage of data 

from more recent accidents, and to incorporate factors in the modeling of tank car performance 

that were not addressed by the analysis in RA-05-02. 

The new estimates are more reflective of current and future tank cars and accident 

environments. The RA-05-02 dataset included accidents that occurred in the period 1965-1997. 

The TWP-17 analysis uses a more up-to-date dataset that extends through 20115

 and excludes 

older data that are considered less relevant to current assessments of tank car safety performance. 

Also, during the discussions of an Association of American Railroads (AAR) Tank Car 

Committee task force6

 and other activities, certain variables were identified as possibly affecting 

tank car accident performance that had not been explored in RA-05-02, such as tank inside 

diameter, jacket standoff distance, the presence of heater coils, new variables that measure the 

severity of the accident environment, and others. Additionally, some variables that were 

evaluated in RA-05-02 had not been incorporated directly into the regression analyses that 

produced the CPR estimates then, but instead were addressed by ad hoc side analyses. In 

TWP-17, they were included directly as independent variables in the regressions, yielding a more 

robust evaluation of the effects of those factors. The most prominent example of this is train 

speed at the time of derailment. 

 

5

 Although much of the crude oil fleet was built after this date, the probability estimates for these cars are valid, 

because all of the features on these cars had been present in the fleet for many years and are well-represented in the 

dataset. More discussion of this issue can be found in section 2(e). 

6

 AAR Tank Car Committee Docket T87.5, “Consider Head and Shell Requirements for Non-Pressure Cars 

Transporting Packing Group I and II Materials”. 
RA-19-01 

February 2019 

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Finally, the identification of significant variables and the determination of coefficients for 

those variables were accomplished in TWP-17 using more sophisticated statistical approaches 

than had been possible in RA-05-02. These techniques allow more robust coefficient estimation 

in cases where the dataset is complex. 

 Characterization or prediction of a single accident is not an objective of CPR analysis. 

CPR estimates predict the average behavior of a given car configuration over a group of 

accidents with similar conditions, and therefore can be used to compare predicted performance 

among car options. There are numerous factors in any individual accident that can cause a car's 

performance to diverge from the average performance over all circumstances. Appropriate uses 

of CPR estimates include incorporating quantitative performance data into risk assessments and 

supporting the benefits calculations in cost-benefit analyses aimed at selecting among a variety 

of packaging options. 

 This study presents the best understanding of statistical tank car accident performance, 

with respect to impact resistance, that could be developed when it was conducted. CPR 

estimates, as with any statistically derived estimates, are potentially subject to change over time, 

as accident environments evolve along with equipment and operating practices, as more and 

newer data come in, and as research continues. The intent is to present CPR estimates that will 

be useful tools now and moving forward, until updates or refinements are desired. 

2. Approach 

a) Definition of “conditional probability of release” 

A conditional probability is the probability of a specific event occurring, given that a specific 

condition is true. For the purpose of this report, the conditional probability of release (CPR) 

for a tank car is the probability that that single tank car releases any quantity7

 of lading, given 

that it is derailed in an FRA-reportable8 accident. 

b) Analytic team 

The TWP-17 analysis was conducted by a team consisting of experts on tank car safety data, 

statistics, and structural reliability at the University of Illinois at Urbana-Champaign, led by 

Dr. Christopher P.L. Barkan, Dr. M. Rapik Saat, and Laura Ghosh, along with Dr. Steve 

Kirkpatrick of Applied Research Associates and Todd Treichel of the Tank Car Safety 

Project. 

c) Data used in the study 

The source of the data used in this study was the Tank Car Safety Project’s database of tank 

cars damaged in accidents. The database contains records on tank cars that were damaged in 

 

7

 A modification wherein only releases above a certain quantity are considered will also be discussed. 

8

 The Federal Railroad Administration requires that railroads report any accident that causes damage to track, 

equipment and/or structures exceeding a certain dollar threshold that is adjusted each year. 
RA-19-01 

February 2019 

3 

derailments and collisions, but only those cars for which the damage was incurred on tankcar-specific features, including the tank, fittings, jacket, head shields, and so on. For more 

information on this database, see Appendix A. Some additional data sources that were drawn 

upon for specific purposes outside of the main analytical calculations are described in 

Appendix E. 

Cars in the Tank Car Safety Project data were included in the study dataset if they met the 

following criteria: 

• Accident occurred 1980 through 2011, the latest year for which complete data were 

available at the time of the analysis 

• Car was built 1970 or later 

• Loaded cars only 

• Cars with shelf couplers only 

• Stub-sill cars only 

• Tank car classes DOT/TC-111, -105, -112, -114, -120, AAR-211 only 

• Tank steel specifications TC128B, A515, A516 only 

• Truck capacity 100 tons or more, and 4 axles only 

• All key fields had known values 

Cars that were damaged only by fire and not by impact, or that released lading only because 

of fire exposure, were excluded. This study focuses strictly on the effects of immediate 

impacts during a derailment. 

These criteria are essentially the same as those used in the RA-05-02 study, apart from the 

time frame. 

As explained below, four analyses were conducted, one for each component of the car that 

can lose lading in an accident. The number of records used in each of the analyses, based on 

the criteria given above, were as shown in Table 1: 

Table 1 

The Number of Tank Car Records Used in Each Component Regression 

And the Number of Accidents in which Those Cars Were Damaged 

Component Tank Cars Accidents 

Shell 7,165 4,993 

Head 4,467 2,464 

Bottom Fittings 5,484 3,905 

Top Fittings 4,467 2,175 

The differences in sizes among these datasets are due to unknowns in data fields that 

eliminated the record from one analysis but not the others. There are fewer accidents than 

cars because some accidents provided more than one car to the analyses. 
RA-19-01 

February 2019 

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d) Identification of variables for regression 

The initial set of independent variables (i.e., potential factors that could affect CPR), as 

reflected in the four full models, was as follows: 

1) Accident-related independent variables 

– Track type (main & siding, or yard & industrial) 

– Accident type (derailment vs. collision) 

– Train speed (mph) 

– Train speed squared (mph2

) 

– Estimated effective impact speed (mph) 

– Estimated effective impact speed squared (mph2) 

– Impact opportunity factor (unit-less score) 

– Number of freight cars derailed 

– Date of accident 

– Various interactions among these variables 

Notes on accident-related variables: 

- Mainline and siding accidents were grouped because track and operational conditions 

are generally similar between the two track types. Similarly, yard accidents and 

industrial track accidents were grouped. 

- Effective impact speed and impact opportunity factor are variables specifically 

developed for this study, and defined below. These and the number of freight cars 

derailed are intended as proxies for the amount of impact energy available for 

damaging a specific tank car in the accident. Although these proxies are not precise 

models for the behaviors they represent, they help the regression calculation to 

attribute different outcomes for otherwise apparently similar cars to varying amounts 

of available impact energy, rather than forcing these differences to be attributed to 

variables that are not actually driving them, i.e., they allow the regression to do a 

better job of evaluating the car characteristics of the most interest. 

- Date of accident was included to capture any trends or changes in the accident 

environment over time that were not captured by other variables. 

- The specific interactions included can be seen in the output from the statistical 

software package, provided in Appendix C. 

2) Car-related independent variables 

– Shell thickness (inches) 

– Shell material type (steel specification TC128B, A516, or A515)

– Shell inside diameter (inches) 

– Head thickness (inches) 
RA-19-01 

February 2019 

5 

– Head material type (steel specification TC128B, A516, or A515) 

– Head shield presence/type (none, half-height, full-height) 

– Jacket (yes/no) 

– Insulation thickness (jacket standoff; inches) 

– Tank capacity (gallons) 

– External heater coils (yes/no) 

– Top fittings type (pressure-car-style protective housing or not) 

– Bottom fittings (equipped yes/no) 

– Lading group (as a proxy for internal pressure) 

– Year car built 

– Car age at time of derailment 

– Interactions among these variables 

Notes on car-related variables: 

- There were 51 records for cars that were known to have had trapezoidal head shields, 

which was not enough to segregate their performance from that of half-height head 

shields that are attached to the tank or integral to the jacket. 

- Insulation thickness includes a thermal protection blanket if present. 

- The only two top fittings configurations with sufficient data for the analysis were 

non-pressure car fittings with no derailment damage prevention system, and fittings 

enclosed in a pressure-car-style protective housing per 49 CFR 179.100-12. 

Although there are now numerous other definitions of top fittings protection, the 

results for the CPR performance of top fittings protection in this study are the best 

available for applying to all of these systems at this time. 

- Lading groups were created by grouping ladings with similarity in 

a) internal pressure in the tank, because of previous impact simulations that 

indicated that this factor could be significant [Ref. 3], and in 

b) temperature in transportation, in case this might affect the performance of the 

steel. 

However, because the results were internally inconsistent and destabilized the 

CPR estimates, the lading groups were dropped from the final analysis. 

- Bottom fittings protection is only addressed in terms of setting the CPR for bottom 

fittings to zero when they are absent from a car. The vast majority of cars with 

bottom fittings have AAR Level A protection, so there is little need to evaluate the 

effects of different levels, and little data to support an analysis of the uncommon B 

and C levels. New bottom outlet handle securement approaches have not been in the 

fleet long enough for there to be sufficient data to analyze those, either. 
RA-19-01 

February 2019 

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- The specific interactions included can be seen in the output from the statistical 

software package, provided in Appendix C. 

- Uncommon or hypothetical tank thicknesses can be analyzed with the head and shell 

formulas derived in this study. The regression process fits a curve, and it is not 

necessary to have empirical data at every value that might undergo analysis. Good 

overall fit and predictive capabilities of the final model will preserve the accuracy of 

estimates for interim thicknesses. Thicknesses that extrapolate beyond the limits of 

the study’s dataset require more care. Typically, values that are beyond but not far 

from the dataset range can be analyzed with good confidence, but the farther out the 

value lies from the dataset’s range, the more caution must be taken. 

3) Variables Considered but Not Included 

The following variables were considered for inclusion, but omitted from the analysis for 

the reasons noted. 

- Additional tank materials beyond TC128B, A515, A516 – Data exploration prior to 

analysis found that there were too few records for other materials, and many (other 

than stainless steel) are of little current interest. 

- Normalization of the tank – The status of a significant fraction of tanks in the study 

was uncertain. Also, previous studies have found that normalization has a minimal 

effect on the likelihood of a failure (see Ref. 2). 

- Ambient temperature – It was decided that commodity was a better proxy for internal 

pressure, and that ambient temperature was not a reliable proxy for tank material 

temperature because of the range of loading temperatures. Likewise, geographic 

location and season were rejected as not being reliable enough indicators of the 

temperatures that the tank steel would be exposed to. 

- Train weight, train length – The available energy in the accident environment for the 

derailed tank cars generally comes from a more localized portion of the train, not the 

entire consist. 

- Outage – The information was not available in the Tank Car Safety Project database, 

and there was no reliable source for this information for individual cars, especially 

given that outage changes during transportation. 

- Loaded vs. Residue – Loaded is the more important case for safety analysis, due to 

the higher quantities of lading available to spill. Residue cars were excluded for 

homogeneity. 

- Tank Class – A single class can encompass a variety of features; specifying actual 

features was regarded as more directly related to performance. 
RA-19-01 

February 2019 

7 

- Additional/specialty car specifications (e.g., DOT/TC-103, -113-, -115, AAR-204) – 

These cars are too different in design and failure modes from the major classes, and 

too few in number to support robust regression analysis. 

- Full sills vs stub sills – There are too few recent full-sill records, which are also 

strongly correlated with certain other features. Full-sill cars were excluded for 

homogeneity. 

- Continuous weld pads on shells – The information was not available in the Tank Car 

Safety Project database, and the effort to identify these was deemed greater than the 

value added to the study. 

- Pressure car top fittings segregated by commodity – This was found to be significant 

in the RA-05-02 analysis, but exploratory data analysis performed early in this study 

did not suggest that this effect would need to be evaluated. 

4) Definition of Effective Impact Speed 

Although any given accident is assigned a speed at which the train derailed in its TCAD 

record and FRA report, the cars derailed in that accident do not all derail at the same 

speed, nor do they impact other objects at the same speed. Their lading loss outcomes are 

affected by this difference. Therefore it was hypothesized that inclusion of a variable to 

account for the difference could improve the modeling of variables of interest, including 

car features. 

A new variable was created to measure this effect for any given accident, called Effective 

Impact Speed, or EIS. 

EIS = TSP × (CDR-TCL+2)/(CDR+1) where (1) 

TSP = reported train speed 

TCL = tank car’s location in derailed string (1 = 1st car derailed, etc.) 

CDR = total number of freight cars derailed 

For cars with unknown position in the derailment, or unknown derailment size, EIS was 

set to TSP/2. 

This formula produces a linear reduction in effective impact speed from the front to the 

back of the derailment. Figure 1 shows an illustrative example: 
RA-19-01 

February 2019 

8 

Figure 1 

Effective Impact Speed (EIS) Curve for a 10-Car Derailment at 40 mph 

The formula does not precisely reflect the differences in real impact speeds, and is not 

intended to. Precision is not necessary because the purpose of this variable is not to 

analyze its effect on outcomes per se, but to give the regression process an additional data 

input to use in explaining some of the variation in outcomes that arises due to such an 

effect, and to minimize the effect of that variation on the characterization of other 

variables. 

5) Definition of impact opportunity factor 

Not all cars in a given accident have the same opportunities to strike or be struck by other 

freight cars. The cars at the front and back of the derailed string have fewer opportunities 

to impact other cars than do those towards the middle. The chance that a car will 

experience an impact capable of leak-causing damage is therefore different within the 

same accident. In order to account for this, a new variable was created, Impact 

Opportunity Factor, or IOF. 

IOF = 1 for single-car derailments 

 = 2 for a car at either end of a multiple-car derailment 

 = 3 for a car one spot inwards from the end of a derailed string of at least 3 

 ....and so on up to maximum of 8 

This formula produces a curve that peaks in the middle of the derailed string. Figure 2 

shows an illustrative example: 

0

5

10

15

20

25

30

35

40

45

0 2 4 6 8 10 12

Effective Impact Speed (mph)

Location of Tank Car within All Cars Derailed
RA-19-01 

February 2019 

9 

Figure 2 

Impact Opportunity Factor Curve for a 15-Car Derailment 

As with EIS, the curve does not precisely reflect the behavior of impact opportunities, but 

it does not need to in order to improve the regression. 

6) Advanced variable selection approach 

The power of regression is undermined when the independent variables are closely 

correlated. This is because the process is unable to determine which of two correlated 

variables is more responsible for a given car’s outcome. These datasets do have 

correlated variables. For example, in the time period under consideration, head shields 

were far more likely to be found on cars with higher tank thickness than with lower 

thickness. 

To minimize this problem, an advanced variable selection procedure, the group minimax 

concave penalty approach (gMCP), was conducted to identify groups of related variables 

that were more likely to be significant, before beginning each regression. This process 

helps to separate the effects of correlated variables. The technique resulted in more 

robust and accurate CPR estimates than would have been possible without such a step. 

More on gMCP can be found in Appendix B. 

e) Regression approach 

As in RA-05-02, a regression analysis was applied to four logistic regression formulas, or 

models. Each of the formulas selected as most representative of the data generates 

estimated CPRs that are specific to one of four components of the tank car: shell (S), head 

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16

Impact Opportunity Factor

Location of Tank Car in Derailment
RA-19-01 

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10 

(H), top fittings (T) and bottom fittings (B). Accident-caused lading losses come from one 

(or more) of these four components. A graphic representation of this scheme is shown in 

Figure 3. 

Figure 3 

Four Components of a Tank Car That Can Lose Lading 

These component CPRs are then combined using a standard probabilistic formula9

 into a 

CPR for the car as whole: 

CPRCAR = 1 – (1 – CPRH) (1 - CPRS)(1 – CPRT)(1 – CPRB) (2) 

The regression approach begins with an equation relating the outcomes, in this case the 

probability of lading loss, with the independent variables, i.e., explanatory factors that are 

assumed to have a reasonable chance to affect those outcomes. The initial equation is the full 

model, which includes all of the independent variables. Logistic regression is a standard 

technique that is used when the dependent variable being estimated is a proportion, and 

therefore ranges from zero to one, such as a probability estimate. 

The observations in the dataset have values for each explanatory term in the model (tank 

thickness, presence of a jacket, and the others), and binary outcomes of zero or one, e.g., 

released lading from that component, or did not. The logistic regression procedure estimates 

the fraction of further observations, i.e., future derailed cars of a similar nature, that will have 

a value of one, that is, that will release lading. The curve (i.e., subset of significant 

independent variables and associated coefficients) that best explains the observed data and 

best predicts future observations is selected as the final regression equation. The independent 

variables in that final equation, and the coefficients assigned to each such term by the 

regression computation, provide the formula for estimating CPR.

 

9

 Use of this formula assumes that the component CPRs are independent, given a set of accident circumstances. 

This is not strictly true. However, the authors believe that the dependence is not large enough to significantly bias 

the results, and is additionally mitigated by the design of the full models, for example, including shell parameters in 

the top fittings model. 

Tank Head Tank Shell 

Bottom Fittings

Top Fittings
RA-19-01 

February 2019 

11 

The component CPR formulas take the form: 

CPRi = eL (Xi) / [1 + eL (Xi)] × FRA multiplier, where (3) 

 i = index to the car component, i.e., head, shell, top fittings or bottom fittings 

 CPRi = the estimated probability of loss from source i 

 L(Xi) = the calculated logistic regression equation for component i

 FRA multiplier as defined below 

The CPR for the car as a whole then is: 

CPRcar = 1െ	∏ ሺ1 െ 	CPRi ௜ ሻ (4) 

The features and properties of each car in the dataset are incorporated separately into the 

regression. That is, the input to the regression is not a car specification like 

“111A100W1”, but a set of values that precisely describe each car’s actual physical 

characteristics. This approach enables the wide range of characteristics in the fleet to 

enhance the statistical power and robustness of the analysis. Configurations that were not 

common in the dataset, but whose features are common, e.g., DOT-111 with top fittings 

protective housing, or DOT-117, can be analyzed accurately because of the componentby-component approach. 

f) CPR for one-component losses 

Cars that release lading might do so from one of the four components (shell, head, top 

fittings, bottom fittings), or more than one. Equation (3) above shows the formula for the 

CPR for one component, including the cases in which the car releases lading from more 

than one source. If it is desirable to consider releases strictly from one component alone, 

the component CPRs can be converted into mutually-exclusive ones using Equations (5a) 

and (5b): 

CPRj* = CPRj × Πi≠j(1− CPRj), and (5a) 

CPRmult = CPRcar − ∑i CPR j*, where (5b) 

 CPRj* = the exclusive CPR for component j, i.e., releases from j and no other 

component, 

 j = index to the car component for which an exclusive CPR is desired, i.e., head, 

shell, top fittings or bottom fittings only, 

 CPRmult = CPR for releases from more than one source (any combination of two 

or more). 
RA-19-01 

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g) FRA multiplier 

The FRA multiplier adjusts the condition on the probability from “given that the car is 

damaged” (i.e., recorded in the Safety Project accident data) to “given that the car is 

derailed in an FRA-reportable accident”10. This is important when CPR estimates are 

used as part of a larger quantitative risk assessment, and combined with FRA accident 

rates and other data based on that metric. The FRA-compatible probability is the form of 

CPR that is most often used by the industry. 

Calculated as shown in Appendix E, the FRA multiplier is 1.00. However, this has not 

been the case in previous studies, and might not be in the future, or additional work might 

reveal a need for different multipliers for specific contexts, so the term is left in Equation 

(3) to be thorough and accurate. 

h) CPRs adjusted for minimum quantity lost 

In some cases, an analysis using CPRs provides better focus on the questions at hand if 

small releases are excluded from consideration. For example, industry analyses of 

flammable liquid package options in the past few years have excluded releases of 100 

gallons or less from individual tank cars, because the users of the analyses were trying to 

address the risk of large pool fires resulting from substantial releases of flammable 

lading. Releases of 100 gallons or less could not produce this scale of incident, and the 

various package options did not all have the same distribution of loss quantities, so it 

made sense to adjust the CPRs to account for this. 

This adjustment to CPR is calculated by multiplying the unadjusted CPR by the fraction 

of releases for the specific car configuration in question that are over 100 gallons (or any 

other quantity11), based on empirical quantity-lost distributions. 

The approach to handling this is to calculate the CPR according to this formula: 

CPR>X,CAR = 1 – i=H,S,T,B (1 – CPRi×Q(i,X)), where (6) 

 CPR>X,CAR = the quantity-adjusted CPR for the car as a whole, 

 X = the gallon threshold; releases of X gallons or less will be excluded 

from CPR>X,CAR

 i = index to the car component, , i.e., head, shell, top fittings or bottom 

fittings, 

 

10 It sometimes occurs that cars are damaged in a way that qualifies them for inclusion in the Safety Project accident 

database, but does not bring the total cost of the accident up to the FRA reportability threshold. The opposite 

frequently occurs, i.e., a car is derailed as part of an FRA-reportable accident, but not damaged in a way that 

threatens containment of the lading. 11 Note that the quantity-lost distribution data necessary to do this for other quantities are not presented here, and are 

beyond the scope of this report. 
RA-19-01 

February 2019 

13 

 CPRi = the unadjusted component CPR for component i, and 

 Q(i,X) = the probability that a release from component i on the car being 

estimated is greater than X gallons. 

So CPR>X is the probability that a single tank car releases more than X gallons, given that 

it is derailed in an FRA-reportable accident. 

i) Quantity lost 

The quantity of lading lost, given a release, was also analyzed, separately from CPR. The 

study characterized the distribution of lading lost from each of the four car components. 

Initially, regressions were attempted with categories of quantity lost as the dependent 

variable. However, there are far fewer release observations than damaged car 

observations, and not enough to support a robust regression. Therefore empirical 

histograms are provided instead. 

j) Expected Quantity Released (EQR) 

The term expected quantity of release (EQR) represents the average quantity lost per car 

derailed. (Note: It is not the average per car releasing. All non-releasing cars contribute 

zeros to the sum of all losses in the numerator of the calculation, while each releasing car 

contributes its own specific loss quantity to the numerator.) This metric is sometimes 

used instead of CPR for car comparisons. EQR is calculated by combining the four 

component CPRs for a particular car configuration with the quantity-lost distributions for 

each of those components. In principle the general form of such a calculation would be 

EQRi = ∑ ሺCPRc, i ∗ Qc, iሻ ୡୀୌ,ୗ,୘୊,୆୊ (7) 

where 

 EQRi = Expected Quantity Released for car i 

 CPRc,i = CPR for car i and component c = H, S, TF or BF 

 Qc,i = Average quantity lost from releases from component c on car i 

However, some releases occur from multiple components on the same derailed car. 

When an accident data record is created, there is generally no way to determine how 

much of the total loss from the car came from each separate release location, so such data 

are not available. In equation (7) above, losses from multiple components are doublecounted. Therefore, an adjustment must be made. A fifth “component”, or loss source, is 

created: Multiple, for losses from two or more sources. This source will be associated 

with its own average loss quantity. (Note that no effort is made to segregate the different 

pairings and combinations of sources that all contribute to the Multiple category. These 

differences are often small and are relevant to a small percentage of releases, and 

therefore this further adjustment is not necessary.) 
RA-19-01 

February 2019 

14 

If CPR*c designates the probability of a loss from component c alone, then 

 CPR ́c = CPRc × Π n ≠ c (1 – CPRn) (8) 

 where c and n are indices to the principal four sources: H, S, TF, and BF. 

And 

 CPR ́m = CPRcar - ∑ c CPR*c (9) 

where CPRm is the probability of a multiple-source release, and CPRcar is the CPR for the 

whole car. 

These single-source CPRs for the four principal sources and Multiple are mutually 

exclusive, and can therefore be summed to arrive at the overall car CPR. They also allow 

the proper calculation of EQR for car i: 

EQRi = ∑ ሺCPR ́c, i ∗ Qc, iሻ ୡୀୌ,ୗ,୘୊,୆୊,୑ (10) 

Safety features that reduce CPR for a component that experiences relatively small 

releases (e.g., top fittings) will reduce EQR to a smaller degree than they will reduce 

CPR, and to a smaller degree than alternative features that create the same reduction in 

CPR, but for a component that typically experiences larger releases (e.g., shell). 

In practice, a simplifying assumption needs to be made if an analyst is relying on this 

report. The data on release quantities for some car/component combinations are not very 

numerous. Therefore the loss quantity data in the Results section of this report are given 

for pressure cars and non-pressure cars, rather than a more fine-grained selection of cars 

and features. The EQR example is calculated this way. 

Note that this assumes that pressure car ladings are pressurized, and non-pressure car 

ladings are not under high pressure. It is assumed that the foremost reason for differences 

between the two groups of cars in terms of quantities lost given a release has to do with 

internal pressure and differences in lading behavior. If the cars of interest depart from 

these assumptions, for example, flammable liquids transported in DOT-120 cars, then the 

analyst should use the most reasonable assumptions about the distributions of quantity 

lost. 

With this simplified approach, the quantity lost for a given component does not vary with 

the presence or absence of safety features or tank thickness differences. Only the 

component CPR portion of the calculation varies. Protection for those components that 

generally release more lading will still affect the EQR more than protection for 

components that release less. The EQR still is affected by relevant changes to each 

component, and can discriminate appropriately among car options in this regard. 
RA-19-01 

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3. Results 

a) CPR formulas 

The variables that had a significant effect on the four component CPRs in the regressions 

are shown below. Note that “significant” here means statistically significant, i.e., there is 

sufficient evidence in the data to conclude that the factor has a measurable effect on CPR. 

Variables that were not statistically significant have dropped out of the calculated 

regression equations. It should be noted that "statistically significant" is not the same as 

"materially significant". The regression coefficient for a given factor may be small 

enough that the effect of the factor on CPR is quite small, even though we are confident 

that there is a non-zero effect. 

These expressions 1 through 4 below are represented by the term L(Xi) in the CPR 

equation (4) in Section 2(e) above. 

1) Shell CPR formula 

 Coefficient Variable 

LSHELL = 5.6289 (Intercept) (11) 

+ -5.2092 × Shell thickness (inches) 

+ -1.0986 × Jacket (yes=1) 

+ -0.0588 × Shell inside diameter (inches) 

+ -0.0514 × Train speed (mph) 

+ 0.00147 × Train speed squared (mph2

) 

+ -0.0254 × Effective impact speed (mph) 

+ -0.00032 × Effective impact speed squared (mph2) 

+ -0.0953 × Cars derailed 

+ 0.0739 × Impact oppo×tunity factor (scalar) 

+ 0.00729 × Train speed x cars derailed 

+ -0.00009 × Train speed squared x cars derailed 

+ 0.00736 × Effective impact speed x Impact opportunity 

2) Head CPR formula 

 Coefficient Variable 

LHEAD = -1.5145 (Intercept) (12) 

+ -3.0699 × Head shield – Full (yes=1) 

+ -2.8387 × Head shield – Half/jacket (yes=1) 

+ -0.6773 × Head shield – Half/no jacket (yes=1) 

+ -1.6871 × Jacket – no head shield (yes=1) 
RA-19-01 

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+ -0.3447 × Head thickness (inches) 

+ 0.5572 × Heater coils (yes=1) 

+ 0.000433 × Train speed (mph) 

+ -0.2281 × Impact opportunity factor (scalar) 

+ -0.7613 × Derailment vs. collision (Der.=1) 

+ 0.00709 × Train speed x impact opportunity 

3) Top fittings CPR formula 

 Coefficient Variable 

LTOPFTG = 0.5555 (Intercept) (13) 

+ 0.6168 × Shell material A515 (yes=1) 

+ 0.0675 × Shell material A516 (yes=1) 

+ -2.7467 × Shell thickness (inches) 

+ -0.5928 × Jacket (yes=1) 

+ -0.0198 × Shell inside diameter (inches) 

+ -1.0092 × Top fittings protective housing (yes=1) 

+ 0.8004 × Derailment vs collision (Der.=1) 

+ 0.000483 × Effective impact speed squared (mph2) 

+ 0.0195 × Train speed (mph) 

+ -0.00084 × Train speed squared (mph2) 

+ 0.0584 × Impact opportunity (scalar) 

+ -0.0009 × Train speed x cars derailed 

+ 0.00002 × Cars derailed x train speed squared 

+ 0.00004 × Train speed squared x impact opportunity 

4) Bottom fitting CPR formula 

 Coefficient Variable 

LBOTFTG = -2.3275 × (Intercept) (14) 

+ -0.873 × Jacket (yes=1) 

+ -5.2546 × Shell thickness (inches) 

+ 0.00328 × Train speed (mph) 

+ 0.000846 × Train speed squared (mph2

) 

+ -0.0275 × Effective impact speed (mph) 

+ 0.0578 × Cars derailed (integer) 

+ -0.2307 × Impact opportunity factor (scalar) 

+ -0.00003 × Train speed squared x cars derailed 

+ 0.0111 × Effective impact speed x impact opportunity 

Note if the car is not equipped with bottom fittings, then CPRBOTFTG is automatically set 

to zero. 
RA-19-01 

February 2019 

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A few of the factors in these formulas are less intuitive than others at first consideration. 

For example, the presence of heater coils appears in the Head CPR formula, even though 

heater coils are not applied to tank heads. Perhaps heater coils affect the way that shells 

and heads interact to absorb energy during an impact; however, this would require more 

study to confirm or explain. But in a regression done in conjunction with gMCP, groups 

of related variables identified as important by that pre-regression process are included 

together unless there is a strong reason not to do so. These must be interpreted as a group 

for the following reason. Heater coils appear on jacketed cars, and jacket, head shield 

type and head thickness form a complex group of correlated factors that are all related to 

head puncture resistance. In such cases, the gMCP reduces the impact of correlations 

among the variables, but cannot eliminate it. (Note too that although the effect of coils is 

statistically significant, it is minimal; for a typical DOT-111, the CPR>100 goes from 

0.196 to 0.189 when coils are added.) 

Another way that gMCP treats a group of variables together is when it uses an interaction 

term to temper the effect of a main-effect factor. This can result in a counter-intuitive 

coefficient sign on some factors. For example, the coefficient on the Impact Opportunity 

Factor in the Head model is negative, apparently implying that CPR for a given tank car 

will go down as the number of derailed cars around the tank car (i.e., that it could 

potentially be impacted by) increases, which is counter-intuitive. However, this factor in 

this model is tied together with train speed by an interaction term, and the collective 

effect works in the direction that one would intuitively expect. There are several possible 

explanations for this analytic result. First, the calculations determined that the overall fit 

of the resulting formula to the data is best when these are the coefficients. Secondly, 

there could be complex effects at work that are beyond the capability of these 

formulations to reflect. For example, some derailments unfold in a linear fashion, while 

others form the common “accordion” pattern. The opportunities for heads to be damaged 

are different in these scenarios, and they may occur under different conditions, including 

train speed. More work would need to be done to settle whether phenomena like that are 

at work. In the shell model, train speed, cars derailed, and effective train speed receive 

negative coefficients. Again, interaction terms involving these three factors (and with 

other variables) are included in the model, and the collective effect works in the expected 

direction. CPRs move in the expected direction when any of these factors is increased or 

decreased. Taken collectively, the effects are logical. If this were not the case in this 

study, the example CPR estimates shown in Table 2 below and elsewhere would produce 

illogical comparisons, but they do not. 

A few other inclusions may need explanation. The formulas consistently find little effect 

from tank steel specification. This is consistent with previous research using empirical 

accident data (Ref. 4). However, in the top fittings model, A515 steel is found to 

significantly differ from A516 or TC128B, and there is a modest difference between 

A516 and TC128B (Note that TC128B was indicated by setting the A515 and A516 

variables to zero). This may be due to the effects on top fittings from the behavior of the 

tank and fittings nozzle, but more work would be needed to explore the cause. In any 

event, the result is not counter-intuitive and there is no evident reason to remove the 
RA-19-01 

February 2019 

18 

factor, so it has been retained. (The overall CPR effect of the variable is again modest 

but not totally negligible; see for example the difference between DOT-111s with TC-128 

tanks vs, A516 in Table 4 below, which is attributable to this factor in this model.) 

Shell thickness has a significant effect on bottom-fittings CPR, and this also deserves 

explanation, as it might be thought that all cars with bottom fittings would have the same 

tank thickness, thereby preventing an effect from that variable being found. Although a 

substantial majority (about 90%) of the cars in the database that were equipped with 

bottom fittings had the same shell thickness, 7/16”, not all of them did. The remaining 

10% (over 500 cars) had thicker shells, which is enough to allow the regression to 

determine an effect. For example, there are 159 cars with bottom fittings and a shell 

thickness of 5/8” and only three of these cars had bottom fittings losses (1.9%), compared 

to 3.0% for 7/16” cars. The data robustly support this finding. 

b) CPRs for common tank cars and other cars of interest 

Table 2 shows mainline CPR estimates for a variety of common tank cars and other cars 

of interest, based on the assumed configurations given. The following accident details 

are also assumed, based on the average mainline freight train accident reported to FRA 

from 2003 to 2012: train speed of 26 mph, 11 cars derailed, the tank car is the 6th car 

derailed. (Variations in these assumptions would change the CPR estimates in accord 

with the component CPR formulas.) Also assumed for comparative purposes is that the 

first car derailed was the first freight car in the train. The latter assumption affects only 

the EIS calculation, and any value could have been chosen as long as it was held constant 

from one estimate to the next. 
RA-19-01 

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Table 212

CPRs and CPR>100s for Selected Tank Cars 

Under Average Mainline Derailment Conditions 

Car Specification Head and 

Shell 

Thickness 

(in.) 

Head and 

Shell Steel 

Type 

Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

Shell 

Inside 

Diameter 

(in.) 

CPR CPR>100

111A100W1 0.4375 A516 No No No Yes 119 0.274 0.20013

111A100W1/3 0.4375 A516 Yes No No Yes 119 0.134 0.089 

111A100W1/2 0.4375 A516 No No No No 119 0.265 0.194 

111A100W1/2/3 0.4375 A516 Yes No No No 119 0.130 0.086 

111A100W2 0.5625 A516 No No Yes No 100.625 0.201 0.167 

111A100W1 0.4375 TC128B Yes Full Yes Yes 119 0.064 0.046 

111A/S100W1 0.500 TC128B No Half Yes Yes 119 0.132 0.103 

117R100W 0.4375 A516 Yes Full No14 Yes 119 0.126 0.081 

117R100W 0.4375 TC128B Yes Full Yes Yes 119 0.064 0.046 

117R100W 0.500 A516 Yes Full No14 Yes 119 0.106 0.067 

117R100W 0.500 TC128B Yes Full Yes Yes 119 0.052 0.037 

117J100W 0.5625 TC128B Yes Full Yes Yes 119 0.042 0.029 

112J340W 0.625 TC128B Yes Full Yes No 118.75 0.033 0.023 

105J300W 0.562 TC128B Yes Full Yes No 118.75 0.040 0.028 

105A500W 0.779 TC128B Yes No Yes No 102 0.040 0.030 

105J500W 0.797 TC128B Yes Full Yes No 102 0.031 0.022 

112J500I H1.03 / S0.89 TC128B Yes Full Yes No 115.34 0.017 0.011 

105J600I H1.136/S0.98 TC128B Yes Full Yes No 106 0.016 0.011 

c) Tank thickness effects 

The results confirm that increased tank thickness reduces CPR, all else being equal. 

Examples can be found in Table 3. Some of these cars are hypothetical, and are only 

included for illustrative purposes. The comparison would change with changes in other 

car and accident factors, but increasing tank thickness always reduces CPR. 

 

12 Table 2 is identical to Table E1 in the Executive Summary. 

13 Preliminary analyses used CPR = 0.266 and CPR>100 = 0.196 for non-jacketed DOT/TC-111 cars. Subsequently 

an adjustment was made to the tank steel assumption that resulted in a slight increase in the CPRs. 14 Specifications for 117R100W require top fittings protection. However, while there are many different types and 

levels of top fittings protection today, the data used for this study did not allow those distinctions to be made 

quantitatively. Top fittings protection was either an impact-resistant protective housing, or none. Some current 

systems probably perform somewhere in between. Therefore, some examples using “No” for this field are presented, 

to suggest the range of performance that the real systems probably fall within. 
RA-19-01 

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Table 3 

CPRs and CPR>100s for Selected Groups of Comparable Tank Cars 

With Different Tank Thicknesses 

Under Average Mainline Derailment Conditions 

Car Spec. Head and 

Shell 

Thickness 

(in.) 

Head and 

Shell Steel 

Type 

Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

Shell 

Inside 

Diameter 

(in.) 

CPR CPR>100

111A100W1 0.4375 A516 No No No Yes 119 0.274 0.200 

111A100W1 0.5000 A516 No No No Yes 119 0.239 0.173 

111A100W1 0.5625 A516 No No No Yes 119 0.208 0.151 

111A100W1 0.6250 A516 No No No Yes 119 0.182 0.133 

105J300W 0.5625 TC128B Yes Full Yes No 118.75 0.040 0.028 

112J340W 0.625 TC128B Yes Full Yes No 118.75 0.033 0.023 

Figure 4 illustrates the general relationship between tank thickness and CPR. The DOT-111 cars 

are assumed to have bottom fittings and 119” inside diameter, and no top fittings protection or 

head shields. 

Figure 4 

Relationship Between Tank Thickness and CPR 

Illustrated for Jacketed and Non-Jacketed 111A100W1 Tank Cars 

Under Average Mainline Derailment Conditions 

d) Tank steel type effects 

The results indicate that there is little difference in empirical CPR performance between 

TC128B steel and A516, but both provide lower CPRs than A515, all else being equal. 

Examples can be found in Table 4. The laboratory performance of TC128B and A516 is 

not equal, but this study finds that the difference in yield strength and other properties 

does not translate into a significant difference in accident performance. This is possibly 

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.3125 0.4375 0.5625 0.6875 0.8125 0.9375 1.0625

CPR

Head and Shell Thickness (in.)

Non‐Jacketed

Jacketed
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because impacts that deliver forces that fall within the interval between the two strengths 

might not dominate the accident environments. Similar studies over the years have found 

the same result. It should be noted that the differences between A516 and TC128B in 

this table are less than the uncertainty surrounding either estimate, i.e., they are not 

statistically significant, although they are directionally consistent with lab data. 

Table 4 

CPRs and CPR>100s for Selected Pairs of Comparable Tank Cars 

With Different Tank Steel Types 

Under Average Mainline Derailment Conditions 

Car Spec. Head and 

Shell 

Thickness 

(in.) 

Head and 

Shell Steel 

Type 

Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

Shell 

Inside 

Diameter 

(in.) 

CPR CPR>100

111A100W1 0.4375 A515 No No No Yes 119 0.354 0.246 

111A100W1 0.4375 A516 No No No Yes 119 0.274 0.200 

111A100W1 0.4375 TC128B No No No Yes 119 0.266 0.196 

112J340W 0.625 A515 Yes Full Yes No 118.75 0.051 0.033 

112J340W 0.625 A516 Yes Full Yes No 118.75 0.034 0.024 

112J340W 0.625 TC128B Yes Full Yes No 118.75 0.033 0.023 

e) Top fittings protection effects 

The results confirm that there are benefits to protecting the top fittings in a damageresistant housing. Table 5 shows one comparison. The comparison would change with 

changes in other car and accident factors, and as noted in the notes on the data in Section 

2(d)(2), there are other top fittings protection systems in the fleet now15 whose 

 15 Another aspect of top fittings can be considered, and further work should be done to determine whether 

an adjustment should be made to account for this. Top fittings protection as defined in this study is a 

pressure car protective housing design, and its performance is based on the accident history with that 

system. Historically, cars with a protective housing were pressure cars, and therefore did not have a 

separate manway; the housing was mounted on a pressure plate that also sealed the manway. On a 

DOT/TC-117 car, on the other hand, the manway generally will be separate from the fittings nozzle. 

Therefore, with respect to top fittings protection overall, the 117 car falls somewhere in between the 111 

car and a pressure car. Based on Tank Car Safety Project data for the study period, 29% of top fittings 

releases from flammable liquid and combustible liquid 111s came from the manway. It may make sense to 

adjust the benefit of top fittings protection for these cars by that amount. However, there are other factors, 

including possible protection due the manway's placement directly adjacent to the robust protective 

housing that might provide some safety benefit in certain types of accident scenarios. Resolution of this 

question will require analysis beyond this study. CPR studies require revisiting and updating over time as 

new or more refined data become available and the TWP-17 study is no exception. When new work 

indicates that CPR estimates need adjustment, supplemental reports will be issued to provide analysts with 

more current data and statistics. 
RA-19-01 

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performance cannot be distinguished in this study. Adding top fittings protection always 

reduces CPR. 

Table 5 

CPRs and CPR>100s for Comparable Tank Cars 

With Different Top Fittings Protection Levels 

Under Average Mainline Derailment Conditions 

Car Spec. Head and 

Shell 

Thickness 

(in.) 

Head and 

Shell 

Steel 

Type 

Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

Shell 

Inside 

Diameter 

(in.) 

CPR CPR>100

111A100W1 0.4375 A516 No No No Yes 119 0.274 0.200 

111A100W1 0.4375 A516 No No Yes Yes 119 0.187 0.151 

117R100W 0.4375 A516 Yes Full No16 Yes 119 0.126 0.081 

117R100W 0.4375 A516 Yes Full Yes Yes 119 0.066 0.047 

Note that the effectiveness of top fittings protection is based on the design being similar 

to the traditional pressure-car-style protective housing described in the federal regulations 

at 49 CFR 179.100-12(c). This is because the CPR estimation is empirically based, and 

this protection design is the only one represented by meaningful numbers of cars in 

TCAD. In recent years, many additional types of top fittings protection have been 

introduced. However, none of these designs have been widespread in the fleet for long 

enough for their effects to be quantifiable. Therefore, at this time, the best estimate of the 

performance of any of these systems is the same estimate that has been derived for the 

traditional pressure-car housing. Future CPR analyses will be better able to distinguish 

between the various top fittings protection approaches. 

The predecessor to this report, RSI-AAR Report RA-05-02 (Ref. 4), found a difference 

between pressure car housings on different specification cars, for example, chlorine cars 

vs. anhydrous ammonia cars. However, in the TWP-17 study, no evidence was found for 

this in the exploratory phase of the project, and the pressure car fittings type variable was 

not selected for inclusion in the full top fittings model. 

f) Jacket effects 

The results confirm that there are significant tank damage resistance benefits to a jacket, 

even though its main purpose is to contain insulation and/or thermal blankets. Table 6 

shows some example comparisons. The comparisons would change with changes in 

other car and accident factors, but the presence of a jacket always confers benefits in this 

regard. Note that the potential effect of the standoff distance, i.e., the distance between 

 

16 Specifications for 117R100W require top fittings protection. However, while there are many different types and 

levels of top fittings protection today, the data used for this study did not allow those distinctions to be made 

quantitatively. Top fittings protection was either an impact-resistant protective housing, or none. Some current 

systems probably perform somewhere in between. Therefore, some examples using “No” for this field are presented, 

to suggest the range of performance that the real systems probably fall within. 
RA-19-01 

February 2019 

23 

the tank and the jacket, was also studied, but this variable was found to not be statistically 

significant. 

Table 6 

CPRs and CPR>100s for Selected Pairs of Comparable Tank Cars 

With and Without Standard 11-Gauge Jackets 

Under Average Mainline Derailment Conditions 

Car Spec. Head and 

Shell 

Thickness 

(in.) 

Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

Shell 

Inside 

Diameter 

(in.) 

CPR CPR>100

111A100W1 0.4375 No No No Yes 119 0.274 0.200 

111A100W1 0.4375 Yes No No Yes 119 0.134 0.089 

111A100W1 0.5 No No No Yes 119 0.239 0.173 

111A100W1 0.5 Yes No Yes No 119 0.114 0.075 

112S340W 0.625 No Half Yes No 118.75 0.091 0.071 

112J340W 0.625 Yes Half Yes No 118.75 0.034 0.023 

g) Head protection effects 

The results confirm that there are benefits to head protection systems, and more benefits 

to full-height protection than for half-height. Table 7 shows some example comparisons. 

The comparisons in Table 7 would change with changes in other car and accident factors, 

but the presence of head protection always confers benefits in this regard. The relative 

benefits are affected by where impacts on the tank head occur (mostly below the 

centerline) and the protective effects of a jacket head or partial jacket head, which is less 

resistant to damage than a head shield, but still offers significant resistance. 

Table 7 

CPRs and CPR>100s for Selected Groups of Comparable Tank Cars 

With Different Levels of Head Protection 

Under Average Mainline Derailment Conditions 

Car Spec. Head and 

Shell 

Thickness 

(in.) 

Head and 

Shell Steel 

Type 

Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

Shell 

Inside 

Diameter 

(in.) 

CPR CPR>100

111A100W1 0.4375 A516 No No No Yes 119 0.274 0.200 

111A100W1 0.4375 A516 No Half No Yes 119 0.252 0.178 

111A100W1 0.4375 A516 Yes No No Yes 119 0.134 0.089 

111A100W1 0.4375 A516 Yes Half No Yes 119 0.127 0.082 

111A100W1 0.4375 A516 Yes Full No Yes 119 0.126 0.081 

112J340W 0.625 TC128B Yes Half Yes No 118.75 0.034 0.023 

112J340W 0.625 TC128B Yes Full Yes No 118.75 0.033 0.023 
RA-19-01 

February 2019 

24 

h) Speed effects (mainline/siding) 

Given a specific tank car configuration, CPRs are lower at lower derailment speeds. Note 

that “derailment speed” means the speed that the train was traveling at the moment of 

derailment, not the impact speed at which an impactor struck the car or the car struck the 

ground. The latter speeds are almost always lower than the derailment speed, but they 

are unknown, so derailment speed must serve as one indicator of how high the impact 

speeds might have been, relatively. Table 8 shows some example comparisons. The 

example speeds of 25 and 40 mph are the speed limits for FRA Class 2 and 3 track, 

respectively. 50 mph is the AAR OT-55 speed limit for key trains [Ref. 1] and the 

regulatory limit for trains meeting the definition of “high-hazard flammable train”. The 

comparisons in Table 8 would change with changes in other car and accident factors, and 

in particular, would change if computed with the average derailment size for a given 

speed, rather than the overall average. 

Table 8 

CPRs and CPR>100s for Selected Cars 

Derailed at Different Speeds 

Under Otherwise Average Mainline Derailment Conditions 

Car Spec. Head and 

Shell 

Thickness 

(in.) 

Head and 

Shell 

Steel 

Type 

Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

Shell 

Inside 

Diameter 

(in.) 

Mph CPR CPR>100

111A100W1 0.4375 A516 Yes No No Yes 119 25 0.132 0.087 

111A100W1 0.4375 A516 Yes No No Yes 119 40 0.176 0.129 

111A100W1 0.4375 A516 Yes No No Yes 119 50 0.241 0.193 

117J100W 0.5625 TC128B Yes Full Yes Yes 119 25 0.041 0.029 

117J100W 0.5625 TC128B Yes Full Yes Yes 119 40 0.064 0.050 

117J100W 0.5625 TC128B Yes Full Yes Yes 119 50 0.102 0.085 

105A500W 0.779 TC128B Yes No Yes No 102 25 0.040 0.030 

105A500W 0.779 TC128B Yes No Yes No 102 40 0.044 0.036 

105A500W 0.779 TC128B Yes No Yes No 102 50 0.066 0.057 

Figure 5 graphically depicts the speed effect on overall car mainline CPR, for nonjacketed 111A100W1s with no additional protective features. Figure 6 shows the same, 

for jacketed cars. In these figures, at each speed, the average derailment size for that 

speed is incorporated into the CPR calculation. 

Note that the speed effect curve does not go through the origin. On the face of it, CPR at 

speeds very near zero mph should also be very near zero. When constructing the models 

for regression, one must choose whether or not to force the intersection to occur at one 

particular point, such as the origin. This can be done, but often at a cost to the goodnessof-fit elsewhere in the data domain. The curve must in a sense be bent away from a 

shape that would fit more data points better, in order to go to the origin. A decision was 

made that the accuracy of analyses at speeds very near zero was less important than the 

accuracy of analyses at typical mainline speeds. Therefore the speed effect was not 

forced through [0,0]. 
RA-19-01 

February 2019 

25 

Figure 5 

Non-Jacketed 111A100W1 Mainline CPR vs. Train Speed 

As Predicted by TWP-17 Formulas, and Empirical Counts 

Subfigure 5a 

TWP-17 CPR Predictions 

Subfigure 5b 

Empirical Lading-Loss Rates 

 

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100 120

CPR (total)

Speed (mph)

B1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0-10 10-20 21-30 31-40 41-50 51-60 61-70

CPR (total)

Speed (mph)
RA-19-01 

February 2019 

26 

Figure 6 

Jacketed 111A100W1 Mainline CPR vs. Train Speed 

As Predicted by TWP-17 Formulas, and Empirical Counts 

Subfigure 6a 

TWP-17 CPR Predictions 

Subfigure 6b 

Empirical Lading-Loss Rates 

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100 120

CPR (total)

Speed (mph)

B2
RA-19-01 

February 2019 

27 

i) Yard/Industrial CPRs 

CPRs on yard or industrial track are always lower than CPRs for the same cars on 

mainline or siding track. However, the variable for track type was not statistically 

significant in any of the component CPR models, so the dominant factors are the lower 

speeds and smaller derailments. Table 9 shows some example comparisons. The average 

derailment conditions for mainline track in the FRA accident data are 26 mph, 11 cars 

derailed, tank car of interest 6th in the derailed string. The average conditions for yards 

are 6 mph, 5 cars derailed and tank car of interest 3rd in the derailed string. 

Table 9 

CPRs and CPR>100s for Selected Cars 

Derailed on Different Track Types 

Under Average Derailment Conditions for Each Type 

Car Spec. Head and 

Shell 

Thickness 

(in.) 

Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

Shell 

Inside 

Diameter 

(in.) 

M= 

Main 

Y= 

Yard 

CPR CPR>100

111A100W1 0.4375 No No No Yes 119 M 0.274 0.200 

111A100W1 0.4375 No No No Yes 119 Y 0.075 0.051 

117J100W 0.5625 Yes Full Yes Yes 119 M 0.042 0.029 

117J100W 0.5625 Yes Full Yes Yes 119 Y 0.010 0.007 

105A500W 0.779 Yes No Yes No 102 M 0.040 0.030 

105A500W 0.779 Yes No Yes No 102 Y 0.007 0.005 

j) Quantity lost results 

Because tank cars have a wide range of capacities, a loss of a given gallon volume can 

represent a different severity of outcome for different cars. For example, a 15,000 gallon 

loss is 50% of the lading from a 30,000 gallon car, but a total loss from a 15,000 gallon 

car. Therefore quantity lost data are represented in this study in terms of percentage of 

car capacity lost. Figure 7 shows the average percentage of car capacity lost in releases 

from each of the four car components, in four sub-tables based on car type and track type. 

The average percent-lost figures for each car/component in Figure 7 are shown with only 

two significant digits in order to avoid presenting a level of precision that may not be 

supportable, given the relatively small number of release accidents available for the 

calculation and the number of factors that can affect the quantity lost. Also, the 

thousandths place on the percentage of a loaded tank represents tens of gallons, and 

generally a round-off at that level will not bias an analysis. 

Figure 8 shows the distribution of loss quantities for each component, broken down into 

five bins of percentages. The bins are not uniform because of how loss quantity 

contributes to risk. For example, very small releases often present a disproportionally 

smaller hazard than 20% or 25% losses, so it is not helpful to lump these together. Table 

10 shows the data behind Figure 8. Note that there are few releases from pressure cars, 

and the distributions shown may not be reliable representations of the relative likelihoods 

of different release sizes. 
RA-19-01 

February 2019 

28 

Figure 7 

Average Quantity of Lading Lost for Each Car Component 

Expressed as a Percentage of Car Capacity 

Subfigure 7a 

Non-Pressure Cars, Mainlines and Sidings 

Subfigure 7b 

Non-Pressure Cars, Yards and Industrial Track 
RA-19-01 

February 2019 

29 

Subfigure 7c 

Pressure Cars, Mainlines and Sidings 

Subfigure 7d 

Pressure Cars, Yards and Industrial Tracks 

 
RA-19-01 

February 2019 

30 

Figure 8 

Distribution of Quantity of Lading Lost, Expressed as a Percentage of Loaded Quantity, for Each 

Car Component 

(Bar Color Indicates Category of the Quantity Lost, as a Percentage) 

Subfigure 8a 

Non-Pressure Cars, Mainline and Sidings 

Subfigure 8b 

Non-Pressure Cars, Yards and Industrial Tracks 
RA-19-01 

February 2019 

31 

Subfigure 8c 

Pressure Cars, Mainline and Sidings 

Subfigure 8d 

Pressure Cars, Yards and Industrial Tracks 

Table 10 provides the count data displayed as percentages in Figure 8. 
RA-19-01 

February 2019 

32 

Table 10 

Number of Tank Cars that Lost Lading, by Percent of Tank Capacity 

Subtable 10a 

Non-Pressure Cars on Mainlines and Sidings 

Percent of Capacity Lost 

Loss Source 0-5 5-20 20-50 50-80 80-100 Total Cars 

H 17 4 18 24 38 101 

S 28 26 34 54 146 288 

T 106 29 43 35 75 288 

B 23 3 2 3 15 46 

M 153 30 30 2 26 241 

Total Cars 327 92 127 118 300 964 

Subtable 10b 

Non-Pressure Cars, Yards and Industrial Tracks 

Percent of Capacity Lost 

Loss Source 0-5 5-20 20-50 50-80 80-100 Total Cars 

H 4 6 8 7 25 50 

S 14 1 3 3 4 25 

T 10 2 0 0 1 13 

B 94 3 3 1 0 101 

M 84 8 12 3 4 111 

Total Cars 206 20 26 14 34 300 

Subtable 10c 

Pressure Cars, Mainlines and Sidings 

Percent of Capacity Lost 

Loss Source 0-5 5-20 20-50 50-80 80-100 Total Cars 

H 1 0 1 1 2 5 

S 2 2 3 0 12 19 

T 6 0 0 0 0 6 

B 0 0 0 0 1 1 

M 6 1 2 3 7 19 

Total Cars 15 3 6 4 22 50 

Subtable 10d 

Pressure Cars, Yards and Industrial Tracks 

Percent of Capacity Lost 

Loss Source 0-5 5-20 20-50 50-80 80-100 Total Cars 

H 1 0 0 0 1 2 

S 2 0 0 1 2 5 

T 0 0 0 0 0 0 

B 0 0 0 0 0 0 

M 9 0 0 0 0 9 

Total Cars 12 0 0 1 3 16 
RA-19-01 

February 2019 

33 

  

k) Expected Quantity Released (EQR) example 

To illustrate why EQR calculations might be of interest, here is an example in which a 

non-jacketed 111A100W1 tank car with a bottom outlet is compared to 1) the same car 

with the bottom outlet removed, 2) the same car with top fittings protection added, and 3) 

the same car with a jacket added. Table 11 displays CPR and EQR estimates for these 

three cars. Note that the percentage of improvement can vary significantly for the same 

risk reduction measure, depending on the performance metric used. 

Table 11 

EQRs, CPRs and CPR>100s for 30,000-Gallon DOT-111 Tank Cars 

With Different Risk Reduction Options (RROs) 

(7/16” Tanks, 119” Shell Inside Diameter) 

Under Average Mainline Derailment Conditions 

Car Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

CPR % 

Reduction 

CPR>100 % 

Reduction 

EQR 

(gals.) 

% 

Reduction 

Base No No No Yes 0.274 n/a 0.200 n/a 3,120 n/a 

RRO1 No No No No 0.257 3.4 % 0.189 3.6% 3,026 3.0 % 

RRO2 No No Yes Yes 0.183 31.2 % 0.149 24.0 % 2,613 16.3% 

RRO3 Yes No No Yes 0.128 51.9 % 0.085 56.6 % 1,199 61.6 % 

RRO1 = Remove bottom fittings 

RRO2 = Add top fittings protection 

RRO3 = Add jacket to head and shell 

EQRs in Table 11 are based on the shell-full capacity of the tanks, i.e., 30,000 gallons in this 

case. For purposes of comparisons among car options with the same tank capacity, this is the 

simplest approach. For other analyses, it might be important to focus on the actual gallons 

loaded, or the estimated gallons of lading at a typical point in transit, or the tons (which do not 

vary during the trip). Note that the reported loss quantities from accidents, which the fractions in 

Figure 7 are based upon, come from cars that have been in transit for some period of time. 

Vapor lost from the tank is generally not part of the reported loss quantity unless vapor is all that 

is lost (for example if a fitting is damaged but is above the liquid level so that only vapor is lost). 

The analyst will need to consider the best approach for a given study. 
RA-19-01 

February 2019 

34 

4. References

1. Association of American Railroads. “Recommended Railroad Operating Practices for 

Transportation of Hazardous Materials, Circular No. OT-55-Q (CPC-1337)”. 6 September 

2018. 

2. Hughes, J.P., C.F. Heuer and T.L. Anderson. “Fracture Behavior of Tank Car Steels in 

Accidents from 1981 through 1994. RSI-AAR Railroad Tank Car Safety Research and Test 

Project Report RA-03-6-62. December 1998. 

3. Kirkpatrick, S. W. “Detailed Puncture Analyses of Tank Cars: Analysis of Different 

Impactor Threats and Impact Conditions.” DOT/FRA/ORD-13-17. March 2013. 

4. Treichel, T.T., J.P. Hughes, C.P.L. Barkan, R.D. Sims, E.A. Phillips, and M.R. Saat. “Safety 

Performance of Tank Cars in Accidents: Probabilities of Lading Loss”. RSI-AAR Railroad 

Tank Car Safety Research and Test Project Report RA-05-02. January 2006. 
RA-19-01 

February 2019 

A-1 

Appendix A 

Tank Car Safety Project Collection of Data on Tank Cars Damaged in Accidents 

The source of the data used in this study was the Tank Car Safety Project’s database of tank cars 

damaged in accidents, known as the Tank Car Accident Database, or TCAD. The database contains 

records on tank cars damaged in derailments and collisions, for which the damage was incurred on 

tank-car-specific features, including the tank, fittings, jacket, head shields, and so on. If there was no 

damage to these features, the car is not included in TCAD, even if there was damage to running gear, 

safety appliances, brake equipment, etc. 

TCAD includes data on any tank cars damaged in the United States or Canada, regardless of 

specification, design features, lading (including non-regulated materials), load/residue status, and 

whether or not lading was released in the accident. 

 The Tank Car Safety Project began collection and analysis of accident data in 1970. At the time 

of publication of this report, TCAD contained records on almost 47,000 damaged tank cars and just 

over 30,000 associated accidents. Not all of these are used in any one analysis. The set of cars used in 

TWP-17 is described in the Approach section of the main report.

 For each car TCAD contains data in three categories: 37 fields describing the accident that 

damaged the car, 40 fields describing the car’s features and lading, and 34 fields describing the damage 

to and performance of the car. 

 These data are collected from 28 disparate sources, including public data reported to FRA and 

PHMSA, proprietary data provided by car owners, car builders and railroads, NTSB, TSB and FRA 

investigations, Tank Car Safety Project accident investigations, and others. Engineers experienced in 

assessing tank car damage collate whichever of these sources are available for a particular car, resolve 

conflicts and gaps, and record an accurate summation of the event. 
RA-19-01 

February 2019 

B-1 

Appendix B 

gMCP 

The power of regression is undermined when the independent variables are closely correlated. 

This is because the process is unable to determine which of two correlated variables is more 

responsible for the outcome. These datasets do have correlated variables. For example, in the 

time period under consideration, head shields were far more likely to be found on cars with higher 

tank thickness than with lower thickness. 

To minimize this problem, an advanced variable selection procedure, the group minimax concave 

penalty approach (gMCP), was conducted to identify groups of related variables that were more 

likely to be significant, before beginning each regression. This process helps to separate the 

effects of correlated variables. It also allows both related groups of variables and individual 

variables to be selected for their importance. The technique resulted in more robust and accurate 

CPR estimates than would have been possible without such a step. 

In brief, gMCP optimizes an objective function with respect to a single group of related variables 

at a time, cycling through the groups until convergence is reached. The process includes all 

variables in groups at first, then considers them individually for exclusion. Whether an individual 

variable enters the regression model is affected by both its own explanatory value and that of its 

group. 

Note that coefficients with confidence limits encompassing zero, and therefore considered not 

significant in unmodified regression, are often left in the final model with this approach if they 

were identified as significant in the group selection process. This is because the process shrinks 

coefficients towards zero, trading some bias for prediction accuracy, and the usual statistical tests 

must be adjusted. Such variables still explain some of the variation. 

Technical details of the approach used are: 

- A coordinate descent algorithm was used, 

- Continuous variables were standardized to have variance = 1, 

- Continuous variables were transformed to center on zero, 

- 10-fold cross-validation applied to help counter the possibility that a global minimum is 

not found, and 

- Where interaction terms were included, both main effects were included as well. 

The gMCP process was chosen after an attempt with LASSO (least absolute shrinkage and 

selection operator) had mixed results. 

The principal diagnostics used in the gMCP process for selecting the best groupings to include were 

- Bayesian Information Criterion (BIC) 

- Akaike Information Criterion (AIC) 

- Generalized cross-validation (GCV) 

- 10-fold cross-validation error (CVE) (six different orders)
RA-19-01 

February 2019 

C-1 

Appendix C 

Final Model Output, Model Fit and Diagnostics 

Following are the computational outputs for the final selected regression models for the four car components. In all 

cases the computational procedure was SAS PROC LOGISTIC. 

For the regressions, the following diagnostic guidelines were followed: 

- The coefficients and associated odds ratios needed to be interpretable. 

- The Hosmer-Lemeshow test for goodness-of-fit had to be passed. 

- The concordance index and ROC curves had to indicate sufficient predictive accuracy. 

- Outliers and high-influence points had to be sparse. 

- Strong correlations among variables had to have been addressed by the gMCP process. 

- Wald chi-square statistics were examined, even where the gMCP suggested retaining 

variables that failed a chi-square test 

Outliers were retained in the dataset. The binary nature of the outcomes limited the influence of 

outliers, and the outlier records were not of the sort that could be rejected as errors. There are many 

variables that affect accident environments, and among thousands of records which account for some 

but not all of these factors, unusual but valid combinations of these factors will arise, even if rarely. 

Finally, outliers made up a small percentage of records anyway, and tended to be evenly distributed 

throughout the domain. Examination of the plots in this chapter supports these conclusions. 

Head 

Model Information 

Data Set WORK.HEADCPR

Response Variable Head_Loss 

Number of Response Levels 2 

Model binary logit 

Optimization Technique Fisher's scoring 

Likelihood Penalty Firth's bias 

correction 

Number of Observations Read 4467 

Number of Observations Used 4467 
RA-19-01 

February 2019 

C-2 

Response Profile 

Ordered 

Value Head_Loss 

Total

Frequency

1 0 4286

2 1 181

Probability modeled is Head_Loss='1'.

Class Level Information 

Class Value 

Design 

Variables 

HSF 0 0 

1 1 

HSHJ 0 0 

1 1 

HSHNJ 0 0 

1 1 

FJKT 0 0 

1 1 

HTR 0 0 

1 1 

ACCTYP 0 0 

1 1 

Intercept-Only Model Convergence Status 

Convergence criterion (GCONV=1E-8) 

satisfied. 

Model Convergence Status 

Convergence criterion (GCONV=1E-8) 

satisfied. 
RA-19-01 

February 2019 

C-3 

Model Fit Statistics 

Criterion 

Intercept 

Only 

Intercept 

and 

Covariates 

AIC 1467.509 1308.031 

SC 1473.914 1378.480 

-2 Log L 1465.509 1286.031 

Testing Global Null Hypothesis: BETA=0 

Test Chi-Square DF Pr > ChiSq

Likelihood Ratio 179.4788 10 <.0001

Score 174.8086 10 <.0001

Wald 141.6655 10 <.0001

Type 3 Analysis of Effects 

Effect DF 

Wald 

Chi-Square Pr > ChiSq 

HSF 1 21.0898 <.0001 

HSHJ 1 11.2014 0.0008 

HSHNJ 1 0.9603 0.3271 

FJKT 1 20.4187 <.0001 

HMT 1 0.0743 0.7851 

HTR 1 2.0189 0.1554 

TSP 1 0.0018 0.9664 

Haz_Env 1 6.3502 0.0117 

ACCTYP 1 8.2247 0.0041 

TSP*Haz_Env 1 10.3836 0.0013 
RA-19-01 

February 2019 

C-4 

Analysis of Maximum Likelihood Estimates 

Parameter DF Estimate 

Standard 

Error 

Wald

Chi-Square Pr > ChiSq

Intercept 1 -1.5145 0.6403 5.5954 0.0180

HSF 1 1 -3.0699 0.6685 21.0898 <.0001

HSHJ 1 1 -2.8387 0.8482 11.2014 0.0008

HSHNJ 1 1 -0.6773 0.6911 0.9603 0.3271

FJKT 1 1 -1.6871 0.3734 20.4187 <.0001

HMT 1 -0.3447 1.2641 0.0743 0.7851

HTR 1 1 0.5572 0.3921 2.0189 0.1554

TSP 1 0.000433 0.0103 0.0018 0.9664

Haz_Env 1 -0.2281 0.0905 6.3502 0.0117

ACCTYP 1 1 -0.7613 0.2655 8.2247 0.0041

TSP*Haz_Env 1 0.00709 0.00220 10.3836 0.0013

Association of Predicted Probabilities and 

Observed Responses 

Percent Concordant 77.5 Somers' D 0.551 

Percent Discordant 22.4 Gamma 0.552 

Percent Tied 0.1 Tau-a 0.043 

Pairs 775766 c 0.776 

Odds Ratio Estimates and Wald Confidence Intervals 

Label Estimate 95% Confidence Limits 

Haz_Env at 

TSP=1 

0.802 0.674 0.954

Haz_Env at 

TSP=2 

0.807 0.681 0.957

Haz_Env at 

TSP=3 

0.813 0.688 0.961

Haz_Env at 

TSP=4 

0.819 0.696 0.964

Haz_Env at 

TSP=5 

0.825 0.703 0.967
RA-19-01 

February 2019 

C-5 

Odds Ratio Estimates and Wald Confidence Intervals 

Label Estimate 95% Confidence Limits 

Haz_Env at 

TSP=10 

0.855 0.741 0.986

Haz_Env at 

TSP=20 

0.917 0.819 1.028

Haz_Env at 

TSP=30 

0.985 0.895 1.084

Haz_Env at 

TSP=40 

1.057 0.960 1.164

Haz_Env at 

TSP=50 

1.135 1.013 1.272

Haz_Env at 

TSP=60 

1.218 1.056 1.406

Haz_Env at 

TSP=70 

1.308 1.095 1.562

TSP at 

Haz_Env=1 

1.008 0.991 1.024

TSP at 

Haz_Env=2 

1.015 1.001 1.028

TSP at 

Haz_Env=3 

1.022 1.011 1.033

TSP at 

Haz_Env=4 

1.029 1.019 1.040

TSP at 

Haz_Env=5 

1.037 1.025 1.048

TSP at 

Haz_Env=6 

1.044 1.030 1.058

TSP at 

Haz_Env=7 

1.051 1.034 1.069

TSP at 

Haz_Env=8 

1.059 1.038 1.080
RA-19-01 

February 2019 

C-6 

Parameter Estimates and Wald Confidence Intervals 

Parameter Estimate 95% Confidence Limits 

Intercept -1.5145 -2.7693 -0.2596

HSF 1 -3.0699 -4.3801 -1.7597

HSHJ 1 -2.8387 -4.5011 -1.1763

HSHNJ 1 -0.6773 -2.0318 0.6773

FJKT 1 -1.6871 -2.4188 -0.9553

HMT -0.3447 -2.8223 2.1329

HTR 1 0.5572 -0.2114 1.3258

TSP 0.00043

3 

-0.0197 0.0206

Haz_Env -0.2281 -0.4055 -0.0507

ACCTYP 1 -0.7613 -1.2817 -0.2410

TSP*Haz_Env 0.00709 0.00278 0.0114
RA-19-01 

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C-7 

Odds Ratio Estimates and Wald Confidence Intervals 

Effect Unit Estimate 95% Confidence Limits 

HSF 1 vs 0 1.000 0.046 0.013 0.172

HSHJ 1 vs 0 1.000 0.059 0.011 0.308

HSHNJ 1 vs 0 1.000 0.508 0.131 1.969

FJKT 1 vs 0 1.000 0.185 0.089 0.385

HMT 1.000 0.708 0.059 8.440

HTR 1 vs 0 1.000 1.746 0.809 3.765

ACCTYP 1 vs 0 1.000 0.467 0.278 0.786
RA-19-01 

February 2019 

C-8 

Estimated Correlation Matrix 

Parameter Intercept HSF1 HSHJ1 HSHNJ1 FJKT1 HMT HTR1 TSP

Intercept 1.0000 0.2361 0.2025 0.2119 0.2660 -0.9180 -0.3742 -0.1869

HSF1 0.2361 1.0000 0.0934 0.0996 0.1628 -0.2982 -0.1381 0.0386

HSHJ1 0.2025 0.0934 1.0000 0.0819 0.1223 -0.2496 -0.1029 0.0268

HSHNJ1 0.2119 0.0996 0.0819 1.0000 0.1511 -0.2572 -0.1276 0.0122

FJKT1 0.2660 0.1628 0.1223 0.1511 1.0000 -0.3468 -0.9020 0.0239

HMT -0.9180 -0.2982 -0.2496 -0.2572 -0.3468 1.0000 0.4014 -0.0604

HTR1 -0.3742 -0.1381 -0.1029 -0.1276 -0.9020 0.4014 1.0000 -0.0179

TSP -0.1869 0.0386 0.0268 0.0122 0.0239 -0.0604 -0.0179 1.0000

Haz_Env -0.1858 0.0456 0.0266 0.0144 0.0511 -0.0785 -0.0237 0.6047

ACCTYP1 -0.0162 -0.0111 -0.0042 0.0021 -0.0256 0.0434 0.0244 -0.4457

TSPHaz_Env 0.1810 -0.0437 -0.0281 -0.0169 -0.0342 0.0800 0.0239 -0.8600
RA-19-01 

February 2019 

C-9 

Estimated Correlation Matrix 

Parameter Haz_Env ACCTYP1 TSPHaz_Env

Intercept -0.1858 -0.0162 0.1810

HSF1 0.0456 -0.0111 -0.0437

HSHJ1 0.0266 -0.0042 -0.0281

HSHNJ1 0.0144 0.0021 -0.0169

FJKT1 0.0511 -0.0256 -0.0342

HMT -0.0785 0.0434 0.0800

HTR1 -0.0237 0.0244 0.0239

TSP 0.6047 -0.4457 -0.8600

Haz_Env 1.0000 -0.5980 -0.8494

ACCTYP1 -0.5980 1.0000 0.4361

TSPHaz_Env -0.8494 0.4361 1.0000

Partition for the Hosmer and Lemeshow Test 

Group Total 

Head_Loss = 1 Head_Loss = 0 

Observed Expected Observed Expected

1 445 0 1.07 445 443.93

2 447 0 2.76 447 444.24

3 448 7 4.74 441 443.26

4 452 2 7.50 450 444.50

5 449 12 10.86 437 438.14

6 438 17 14.19 421 423.81

7 448 25 19.14 423 428.86

8 447 24 23.67 423 423.33

9 447 27 35.12 420 411.88

10 446 67 66.73 379 379.27

Hosmer and Lemeshow 

Goodness-of-Fit Test 

Chi-Square DF Pr > ChiSq 

13.6615 8 0.0910 
RA-19-01 

February 2019 

C-10 
RA-19-01 

February 2019 

C-11 
RA-19-01 

February 2019 

C-12 

Shell 

Model Information 

Data Set WORK.SHELL_

CPR

Response Variable Shell_Loss

Number of Response Levels 2

Model binary logit

Optimization Technique Fisher's scoring

Likelihood Penalty Firth's bias 

correction
RA-19-01 

February 2019 

C-13 

Number of Observations Read 7165

Number of Observations Used 7165

Response Profile 

Ordered 

Value Shell_Loss 

Total 

Frequency 

1 0 6815 

2 1 350 

Probability modeled is Shell_Loss='1'.

Class Level Information 

Class Value 

Design 

Variables 

Shell_Lad_Grp A 0 0 0 0 0 

D 1 0 0 0 0 

G 0 1 0 0 0 

H 0 0 1 0 0 

L 0 0 0 1 0 

O 0 0 0 0 1 

Intercept-Only Model Convergence Status 

Convergence criterion (GCONV=1E-8) 

satisfied.

Model Convergence Status 

Convergence criterion (GCONV=1E-8) 

satisfied.
RA-19-01 

February 2019 

C-14 

Model Fit Statistics 

Criterion 

Intercept 

Only 

Intercept 

and 

Covariates 

AIC 2648.441 1999.073 

SC 2655.318 2122.858 

-2 Log L 2646.441 1963.073 

Testing Global Null Hypothesis: BETA=0 

Test Chi-Square DF Pr > ChiSq

Likelihood Ratio 683.3684 17 <.0001

Score 926.4661 17 <.0001

Wald 561.1429 17 <.0001

Type 3 Analysis of Effects 

Effect DF 

Wald 

Chi-Square Pr > ChiSq 

STS 1 21.0475 <.0001 

JKT 1 53.9564 <.0001 

SID 1 25.1491 <.0001 

TSP 1 2.5472 0.1105 

TSP2 1 8.2004 0.0042 

SEV 1 0.4567 0.4992 

SEV2 1 0.2924 0.5887 

CDR 1 6.1236 0.0133 

Haz_Env 1 0.8297 0.3624 

TSP*CDR 1 19.3758 <.0001 

TSP2*CDR 1 20.9714 <.0001 

SEV*Haz_Env 1 5.2947 0.0214 

Shell_Lad_Grp 5 37.1427 <.0001 
RA-19-01 

February 2019 

C-15 

Analysis of Maximum Likelihood Estimates 

Parameter DF Estimate

Standard 

Error 

Wald

Chi-Square Pr > ChiSq

Intercept 1 5.6289 1.3984 16.2030 <.0001

STS 1 -5.2092 1.1355 21.0475 <.0001

JKT 1 -1.0986 0.1496 53.9564 <.0001

SID 1 -0.0588 0.0117 25.1491 <.0001

TSP 1 -0.0514 0.0322 2.5472 0.1105

TSP2 1 0.00147 0.000514 8.2004 0.0042

SEV 1 -0.0254 0.0376 0.4567 0.4992

SEV2 1 -0.00032 0.000594 0.2924 0.5887

CDR 1 -0.0953 0.0385 6.1236 0.0133

Haz_Env 1 0.0739 0.0811 0.8297 0.3624

TSP*CDR 1 0.00729 0.00166 19.3758 <.0001

TSP2*CDR 1 -0.00009 0.000020 20.9714 <.0001

SEV*Haz_Env 1 0.00736 0.00320 5.2947 0.0214

Shell_Lad_Grp D 1 -0.7976 0.3437 5.3845 0.0203

Shell_Lad_Grp G 1 -0.9089 0.2699 11.3439 0.0008

Shell_Lad_Grp H 1 -0.4355 0.2406 3.2760 0.0703

Shell_Lad_Grp L 1 1.4745 0.3781 15.2044 <.0001

Shell_Lad_Grp O 1 -1.5734 0.6590 5.6993 0.0170

Association of Predicted Probabilities and 

Observed Responses 

Percent Concordant 86.0 Somers' D 0.721

Percent Discordant 13.9 Gamma 0.721

Percent Tied 0.0 Tau-a 0.067

Pairs 2385250 c 0.860
RA-19-01 

February 2019 

C-16 

Odds Ratio Estimates and Wald Confidence Intervals 

Label Estimate 90% Confidence Limits 

TSP at CDR=13.803 1.050 0.998 1.106

TSP2 at CDR=13.803 1.000 0.999 1.001

CDR at TSP=22.24 

TSP2=692.14 

1.003 0.977 1.030

Haz_Env at SEV=12.165 1.177 1.081 1.282

Parameter Estimates and Wald Confidence Intervals 

Parameter Estimate 90% Confidence Limits 

Intercept 5.6289 3.3288 7.9290

STS -5.2092 -7.0769 -3.3416

JKT -1.0986 -1.3446 -0.8526
RA-19-01 

February 2019 

C-17 

Parameter Estimates and Wald Confidence Intervals 

Parameter Estimate 90% Confidence Limits 

SID -0.0588 -0.0781 -0.0395

TSP -0.0514 -0.1045 0.00157

TSP2 0.00147 0.000627 0.00232

SEV -0.0254 -0.0873 0.0365

SEV2 -0.00032 -0.00130 0.000656

CDR -0.0953 -0.1587 -0.0320

Haz_Env 0.0739 -0.0595 0.2073

TSP*CDR 0.00729 0.00457 0.0100

TSP2*CDR -0.00009 -0.00012 -0.00006

SEV*Haz_Env 0.00736 0.00210 0.0126

Shell_Lad_Grp D -0.7976 -1.3629 -0.2322

Shell_Lad_Grp G -0.9089 -1.3528 -0.4650

Shell_Lad_Grp H -0.4355 -0.8312 -0.0397

Shell_Lad_Grp L 1.4745 0.8525 2.0965

Shell_Lad_Grp O -1.5734 -2.6574 -0.4893

Odds Ratio Estimates and Wald Confidence Intervals 

Effect Unit Estimate 90% Confidence Limits 

STS 1.000 0.005 <0.001 0.035

JKT 1.000 0.333 0.261 0.426

SID 1.000 0.943 0.925 0.961

SEV2 1.000 1.000 0.999 1.001

Shell_Lad_Grp D vs A 1.000 0.450 0.256 0.793

Shell_Lad_Grp G vs A 1.000 0.403 0.259 0.628

Shell_Lad_Grp H vs A 1.000 0.647 0.436 0.961

Shell_Lad_Grp L vs A 1.000 4.369 2.345 8.137

Shell_Lad_Grp O vs A 1.000 0.207 0.070 0.613
RA-19-01 

February 2019 

C-18 
RA-19-01 

February 2019 

C-19 

Estimated Correlation Matrix 

Parameter Intercept STS JKT SID TSP TSP2 SEV SEV2 CDR Haz_Env

Intercept 1.0000 -0.2336 -0.3312 -0.8920 -0.0189 -0.0021 -0.1754 0.1426 -0.1402 -0.0919

STS -0.2336 1.0000 -0.2434 -0.1353 -0.0069 0.0020 0.0199 -0.0121 -0.0155 0.0183

JKT -0.3312 -0.2434 1.0000 0.3924 0.0329 -0.0241 -0.0086 0.0274 -0.0218 0.0256

SID -0.8920 -0.1353 0.3924 1.0000 -0.0593 0.0899 0.0735 -0.1012 0.0823 -0.0527

TSP -0.0189 -0.0069 0.0329 -0.0593 1.0000 -0.9264 -0.5110 0.3930 0.1271 -0.3800

TSP2 -0.0021 0.0020 -0.0241 0.0899 -0.9264 1.0000 0.2946 -0.2421 0.0560 0.2192

SEV -0.1754 0.0199 -0.0086 0.0735 -0.5110 0.2946 1.0000 -0.8387 -0.1324 0.4716

SEV2 0.1426 -0.0121 0.0274 -0.1012 0.3930 -0.2421 -0.8387 1.0000 0.0153 -0.0677

CDR -0.1402 -0.0155 -0.0218 0.0823 0.1271 0.0560 -0.1324 0.0153 1.0000 -0.3333

Haz_Env -0.0919 0.0183 0.0256 -0.0527 -0.3800 0.2192 0.4716 -0.0677 -0.3333 1.0000

TSPCDR 0.1304 0.0185 0.0024 -0.0426 -0.3973 0.2718 0.1215 0.0007 -0.9110 0.3333

TSP2CDR -0.0961 -0.0180 0.0012 -0.0064 0.5720 -0.5452 -0.0831 -0.0255 0.6980 -0.2737

SEVHaz_Env 0.1416 -0.0293 -0.0336 -0.0069 0.3323 -0.2047 -0.5512 0.0921 0.2817 -0.8580

Shell_Lad_GrpD -0.3216 -0.4743 0.4515 0.5160 -0.0127 0.0291 0.0249 -0.0385 -0.0220 -0.0431

Shell_Lad_GrpG -0.3307 0.0713 -0.0868 0.3307 0.0232 -0.0279 0.0348 -0.0545 -0.0348 -0.0245

Shell_Lad_GrpH 0.0685 0.1451 -0.2567 -0.1235 -0.0338 0.0439 0.0059 -0.0296 0.0206 -0.0179

Shell_Lad_GrpL 0.3594 -0.3226 -0.1659 -0.2488 0.0210 -0.0159 -0.0262 0.0011 0.0465 -0.0801

Shell_Lad_GrpO -0.1304 0.0310 -0.0468 0.1274 -0.0006 -0.0036 -0.0064 -0.0031 -0.0013 -0.0051

Estimated Correlation Matrix 

Parameter TSPCDR TSP2CDR SEVHaz_Env Shell_Lad_GrpD Shell_Lad_GrpG 

Intercept 0.1304 -0.0961 0.1416 -0.3216 -0.3307 

STS 0.0185 -0.0180 -0.0293 -0.4743 0.0713 

JKT 0.0024 0.0012 -0.0336 0.4515 -0.0868 

SID -0.0426 -0.0064 -0.0069 0.5160 0.3307 

TSP -0.3973 0.5720 0.3323 -0.0127 0.0232 

TSP2 0.2718 -0.5452 -0.2047 0.0291 -0.0279 

SEV 0.1215 -0.0831 -0.5512 0.0249 0.0348 

SEV2 0.0007 -0.0255 0.0921 -0.0385 -0.0545 
RA-19-01 

February 2019 

C-20 

Estimated Correlation Matrix 

Parameter TSPCDR TSP2CDR SEVHaz_Env Shell_Lad_GrpD Shell_Lad_GrpG 

CDR -0.9110 0.6980 0.2817 -0.0220 -0.0348 

Haz_Env 0.3333 -0.2737 -0.8580 -0.0431 -0.0245 

TSPCDR 1.0000 -0.9238 -0.2838 0.0122 -0.0247 

TSP2CDR -0.9238 1.0000 0.2326 -0.0210 0.0576 

SEVHaz_Env -0.2838 0.2326 1.0000 0.0101 0.0125 

Shell_Lad_GrpD 0.0122 -0.0210 0.0101 1.0000 0.1536 

Shell_Lad_GrpG -0.0247 0.0576 0.0125 0.1536 1.0000 

Shell_Lad_GrpH -0.0138 -0.0018 0.0267 -0.0926 0.0972 

Shell_Lad_GrpL -0.0629 0.0686 0.0719 0.0306 -0.0349 

Shell_Lad_GrpO 0.0071 -0.0050 0.0142 0.0451 0.0949 

Estimated Correlation Matrix 

Parameter Shell_Lad_GrpH Shell_Lad_GrpL Shell_Lad_GrpO

Intercept 0.0685 0.3594 -0.1304

STS 0.1451 -0.3226 0.0310

JKT -0.2567 -0.1659 -0.0468

SID -0.1235 -0.2488 0.1274

TSP -0.0338 0.0210 -0.0006

TSP2 0.0439 -0.0159 -0.0036

SEV 0.0059 -0.0262 -0.0064

SEV2 -0.0296 0.0011 -0.0031

CDR 0.0206 0.0465 -0.0013

Haz_Env -0.0179 -0.0801 -0.0051

TSPCDR -0.0138 -0.0629 0.0071

TSP2CDR -0.0018 0.0686 -0.0050

SEVHaz_Env 0.0267 0.0719 0.0142

Shell_Lad_GrpD -0.0926 0.0306 0.0451

Shell_Lad_GrpG 0.0972 -0.0349 0.0949
RA-19-01 

February 2019 

C-21 

Estimated Correlation Matrix 

Parameter Shell_Lad_GrpH Shell_Lad_GrpL Shell_Lad_GrpO

Shell_Lad_GrpH 1.0000 0.0707 0.0367

Shell_Lad_GrpL 0.0707 1.0000 -0.0187

Shell_Lad_GrpO 0.0367 -0.0187 1.0000

Partition for the Hosmer and Lemeshow Test 

Group Total 

Shell_Loss = 1 Shell_Loss = 0 

Observed Expected Observed Expected

1 711 2 2.09 709 708.91

2 717 3 4.37 714 712.63

3 719 6 6.74 713 712.26

4 681 5 8.78 676 672.22

5 704 13 11.51 691 692.49

6 718 1 14.43 717 703.57

7 717 27 18.75 690 698.25

8 668 34 27.96 634 640.04

9 717 53 53.76 664 663.24

10 813 206 207.71 607 605.29

Hosmer and Lemeshow 

Goodness-of-Fit Test 

Chi-Square DF Pr > ChiSq 

20.2341 8 0.0095 
RA-19-01 

February 2019 

C-22 

Classification Table 

Prob 

Level 

Correct Incorrect Percentages 

Event 

NonEvent Event NonEvent Correct SensitivitySpecificityFalse

POS

False

NEG

0.000 350 0 6815 0 4.9 100.0 0.0 95.1 .

0.020 320 4082 2733 30 61.4 91.4 59.9 89.5 0.7

0.040 275 5211 1604 75 76.6 78.6 76.5 85.4 1.4

0.060 244 5724 1091 106 83.3 69.7 84.0 81.7 1.8

0.080 227 5949 866 123 86.2 64.9 87.3 79.2 2.0

0.100 212 6160 655 138 88.9 60.6 90.4 75.5 2.2

0.120 194 6243 572 156 89.8 55.4 91.6 74.7 2.4

0.140 173 6313 502 177 90.5 49.4 92.6 74.4 2.7

0.160 166 6392 423 184 91.5 47.4 93.8 71.8 2.8

0.180 153 6442 373 197 92.0 43.7 94.5 70.9 3.0

0.200 146 6478 337 204 92.4 41.7 95.1 69.8 3.1

0.220 135 6525 290 215 93.0 38.6 95.7 68.2 3.2

0.240 104 6611 204 246 93.7 29.7 97.0 66.2 3.6

0.260 94 6652 163 256 94.2 26.9 97.6 63.4 3.7

0.280 86 6677 138 264 94.4 24.6 98.0 61.6 3.8

0.300 82 6701 114 268 94.7 23.4 98.3 58.2 3.8

0.320 79 6716 99 271 94.8 22.6 98.5 55.6 3.9

0.340 79 6726 89 271 95.0 22.6 98.7 53.0 3.9

0.360 74 6731 84 276 95.0 21.1 98.8 53.2 3.9

0.380 72 6735 80 278 95.0 20.6 98.8 52.6 4.0

0.400 69 6744 71 281 95.1 19.7 99.0 50.7 4.0

0.420 62 6753 62 288 95.1 17.7 99.1 50.0 4.1

0.440 53 6765 50 297 95.2 15.1 99.3 48.5 4.2

0.460 48 6773 42 302 95.2 13.7 99.4 46.7 4.3

0.480 43 6777 38 307 95.2 12.3 99.4 46.9 4.3

0.500 36 6785 30 314 95.2 10.3 99.6 45.5 4.4
RA-19-01 

February 2019 

C-23 

Classification Table 

Prob 

Level 

Correct Incorrect Percentages 

Event 

NonEvent Event NonEvent Correct SensitivitySpecificityFalse

POS

False

NEG

0.520 31 6787 28 319 95.2 8.9 99.6 47.5 4.5

0.540 26 6791 24 324 95.1 7.4 99.6 48.0 4.6

0.560 20 6797 18 330 95.1 5.7 99.7 47.4 4.6

0.580 12 6800 15 338 95.1 3.4 99.8 55.6 4.7

0.600 9 6803 12 341 95.1 2.6 99.8 57.1 4.8

0.620 4 6808 7 346 95.1 1.1 99.9 63.6 4.8

0.640 3 6808 7 347 95.1 0.9 99.9 70.0 4.8

0.660 2 6810 5 348 95.1 0.6 99.9 71.4 4.9

0.680 1 6812 3 349 95.1 0.3 100.0 75.0 4.9

0.700 1 6812 3 349 95.1 0.3 100.0 75.0 4.9

0.720 1 6812 3 349 95.1 0.3 100.0 75.0 4.9

0.740 0 6813 2 350 95.1 0.0 100.0 100.0 4.9

0.760 0 6814 1 350 95.1 0.0 100.0 100.0 4.9

0.780 0 6814 1 350 95.1 0.0 100.0 100.0 4.9

0.800 0 6814 1 350 95.1 0.0 100.0 100.0 4.9

0.820 0 6814 1 350 95.1 0.0 100.0 100.0 4.9

0.840 0 6814 1 350 95.1 0.0 100.0 100.0 4.9

0.860 0 6815 0 350 95.1 0.0 100.0 . 4.9

Top Fittings 

Model Information 

Data Set WORK.TFCPR 

Response Variable TF_Loss 

Number of Response Levels 2 

Model binary logit 

Optimization Technique Fisher's scoring 

Likelihood Penalty Firth's bias 

correction 
RA-19-01 

February 2019 

C-24 

Number of Observations Read 4467 

Number of Observations Used 4467 

Response Profile 

Ordered 

Value TF_Loss 

Total 

Frequency 

1 0 3946 

2 1 521 

Probability modeled is TF_Loss='1'.

Class Level Information 

Class Value Design Variables 

SMS 128 0 0 

515 1 0 

516 0 1 

JKT 0 0 

1 1 

TFT 0 0 

1 1 

ACCTYP 0 0 

1 1 

TF_Lading_Grp A 0 0 0 0 0 0 0 0 0 0 0

B 1 0 0 0 0 0 0 0 0 0 0

D 0 1 0 0 0 0 0 0 0 0 0

E 0 0 1 0 0 0 0 0 0 0 0

F 0 0 0 1 0 0 0 0 0 0 0

G 0 0 0 0 1 0 0 0 0 0 0

H 0 0 0 0 0 1 0 0 0 0 0

K 0 0 0 0 0 0 1 0 0 0 0

M 0 0 0 0 0 0 0 1 0 0 0
RA-19-01 

February 2019 

C-25 

Class Level Information 

Class Value Design Variables 

O 0 0 0 0 0 0 0 0 1 0 0

Q 0 0 0 0 0 0 0 0 0 1 0

T 0 0 0 0 0 0 0 0 0 0 1

Intercept-Only Model Convergence Status 

Convergence criterion (GCONV=1E-8) 

satisfied. 

Model Convergence Status 

Convergence criterion (GCONV=1E-8) 

satisfied. 

Model Fit Statistics 

Criterion 

Intercept 

Only 

Intercept 

and 

Covariates 

AIC 3040.970 2535.692 

SC 3047.375 2702.208 

-2 Log L 3038.970 2483.692 

Testing Global Null Hypothesis: BETA=0 

Test Chi-Square DF Pr > ChiSq

Likelihood Ratio 555.2789 25 <.0001

Score 503.7059 25 <.0001

Wald 353.1420 25 <.0001
RA-19-01 

February 2019 

C-26 

Type 3 Analysis of Effects 

Effect DF 

Wald 

Chi-Square Pr > ChiSq

SMS 2 22.1531 <.0001

STS 1 1.9989 0.1574

JKT 1 17.9973 <.0001

SID 1 1.7225 0.1894

TFT 1 4.1741 0.0410

ACCTYP 1 13.7555 0.0002

SEV2 1 8.1144 0.0044

TSP 1 1.1729 0.2788

TSP*CDR 1 3.0099 0.0828

TSP2 1 3.9557 0.0467

CDR*TSP2 1 3.6516 0.0560

Haz_Env 1 1.5996 0.2060

TSP2*Haz_Env 1 1.5749 0.2095

TF_Lading_Grp 11 114.8696 <.0001

Analysis of Maximum Likelihood Estimates 

Parameter DF Estimate 

Standard

Error

Wald

Chi-Square Pr > ChiSq

Intercept 1 0.5555 1.9739 0.0792 0.7784

SMS 515 1 0.6168 0.2007 9.4462 0.0021

SMS 516 1 0.0675 0.1958 0.1191 0.7300

STS 1 -2.7467 1.9427 1.9989 0.1574

JKT 1 1 -0.5928 0.1397 17.9973 <.0001

SID 1 -0.0198 0.0151 1.7225 0.1894

TFT 1 1 -1.0092 0.4939 4.1741 0.0410

ACCTYP 1 1 0.8004 0.2158 13.7555 0.0002

SEV2 1 0.000483 0.000170 8.1144 0.0044

TSP 1 0.0195 0.0180 1.1729 0.2788

TSP*CDR 1 -0.00090 0.000516 3.0099 0.0828

TSP2 1 -0.00084 0.000423 3.9557 0.0467
RA-19-01 

February 2019 

C-27 

Analysis of Maximum Likelihood Estimates 

Parameter DF Estimate 

Standard

Error

Wald

Chi-Square Pr > ChiSq

CDR*TSP2 1 0.000020 0.000010 3.6516 0.0560

Haz_Env 1 0.0584 0.0462 1.5996 0.2060

TSP2*Haz_Env 1 0.000040 0.000032 1.5749 0.2095

TF_Lading_Grp B 1 0.1975 0.2177 0.8231 0.3643

TF_Lading_Grp D 1 0.8302 0.3485 5.6741 0.0172

TF_Lading_Grp E 1 0.6831 0.2061 10.9844 0.0009

TF_Lading_Grp F 1 0.3576 0.2261 2.5020 0.1137

TF_Lading_Grp G 1 -2.0358 0.4077 24.9345 <.0001

TF_Lading_Grp H 1 -1.8599 0.4182 19.7778 <.0001

TF_Lading_Grp K 1 -0.9286 0.4530 4.2012 0.0404

TF_Lading_Grp M 1 1.1469 0.5453 4.4242 0.0354

TF_Lading_Grp O 1 -1.3968 0.5753 5.8938 0.0152

TF_Lading_Grp Q 1 -1.1367 0.6854 2.7502 0.0972

TF_Lading_Grp T 1 -2.3648 1.4465 2.6728 0.1021

Association of Predicted Probabilities and 

Observed Responses 

Percent Concordant 79.9 Somers' D 0.598

Percent Discordant 20.1 Gamma 0.598

Percent Tied 0.0 Tau-a 0.123

Pairs 2055866 c 0.799

Odds Ratio Estimates and Wald Confidence Intervals 

Label Estimate 95% Confidence Limits 

CDR at TSP=5 

TSP2=25 

0.996 0.991 1.001

CDR at TSP=10 

TSP2=100 

0.993 0.985 1.001

CDR at TSP=15 

TSP2=225 

0.991 0.980 1.002
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February 2019 

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Odds Ratio Estimates and Wald Confidence Intervals 

Label Estimate 95% Confidence Limits 

CDR at TSP=20 

TSP2=400 

0.990 0.978 1.003

CDR at TSP=25 

TSP2=625 

0.990 0.977 1.004

CDR at TSP=30 

TSP2=900 

0.991 0.977 1.005

CDR at TSP=40 

TSP2=1600 

0.996 0.982 1.010

CDR at TSP=50 

TSP2=2500 

1.005 0.989 1.022

CDR at TSP=60 

TSP2=3600 

1.018 0.993 1.045
RA-19-01 

February 2019 

C-29 

Odds Ratio Estimates and Wald Confidence Intervals 

Label Estimate 95% Confidence Limits

TSP at CDR=13.651 1.007 0.980 1.035

TSP2 at CDR=13.651 Haz_Env=4.1511 1.000 0.999 1.000

SEV2 1.000 1.000 1.001

Odds Ratio Estimates and Wald Confidence Intervals 

Label Estimate 95% Confidence Limits

Haz_Env at TSP2=815.08 1.095 1.024 1.171
RA-19-01 

February 2019 

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Parameter Estimates and Wald Confidence Intervals 

Parameter Estimate 95% Confidence Limits 

Intercept 0.5555 -3.3132 4.4243

SMS 515 0.6168 0.2234 1.0101

SMS 516 0.0675 -0.3161 0.4512

STS -2.7467 -6.5543 1.0610

JKT 1 -0.5928 -0.8667 -0.3189

SID -0.0198 -0.0494 0.00978

TFT 1 -1.0092 -1.9773 -0.0410

ACCTYP 1 0.8004 0.3774 1.2234

SEV2 0.000483 0.000151 0.000815

TSP 0.0195 -0.0158 0.0547

TSP*CDR -0.00090 -0.00191 0.000116

TSP2 -0.00084 -0.00167 -0.00001
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C-31 

Parameter Estimates and Wald Confidence Intervals 

Parameter Estimate 95% Confidence Limits 

CDR*TSP2 0.000020 -5.13E-7 0.000040

Haz_Env 0.0584 -0.0321 0.1489

TSP2*Haz_Env 0.000040 -0.00002 0.000103

TF_Lading_Grp B 0.1975 -0.2291 0.6241

TF_Lading_Grp D 0.8302 0.1471 1.5133

TF_Lading_Grp E 0.6831 0.2791 1.0870

TF_Lading_Grp F 0.3576 -0.0855 0.8008

TF_Lading_Grp G -2.0358 -2.8349 -1.2368

TF_Lading_Grp H -1.8599 -2.6796 -1.0402

TF_Lading_Grp K -0.9286 -1.8165 -0.0406

TF_Lading_Grp M 1.1469 0.0782 2.2156

TF_Lading_Grp O -1.3968 -2.5244 -0.2691

TF_Lading_Grp Q -1.1367 -2.4800 0.2067

TF_Lading_Grp T -2.3648 -5.1998 0.4702

Odds Ratio Estimates and Wald Confidence Intervals 

Effect Unit Estimate 95% Confidence Limits 

SMS 515 vs 128 1.000 1.853 1.250 2.746

SMS 516 vs 128 1.000 1.070 0.729 1.570

STS 1.000 0.064 0.001 2.889

JKT 1 vs 0 1.000 0.553 0.420 0.727

SID 1.000 0.980 0.952 1.010

TFT 1 vs 0 1.000 0.365 0.138 0.960

ACCTYP 1 vs 0 1.000 2.226 1.459 3.399

SEV2 1.000 1.000 1.000 1.001

TF_Lading_Grp B vs A 1.000 1.218 0.795 1.867

TF_Lading_Grp D vs A 1.000 2.294 1.158 4.542

TF_Lading_Grp E vs A 1.000 1.980 1.322 2.965

TF_Lading_Grp F vs A 1.000 1.430 0.918 2.227

TF_Lading_Grp G vs A 1.000 0.131 0.059 0.290

TF_Lading_Grp H vs A 1.000 0.156 0.069 0.353
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February 2019 

C-32 

Odds Ratio Estimates and Wald Confidence Intervals 

Effect Unit Estimate 95% Confidence Limits 

TF_Lading_Grp K vs A 1.000 0.395 0.163 0.960

TF_Lading_Grp M vs A 1.000 3.148 1.081 9.167

TF_Lading_Grp O vs A 1.000 0.247 0.080 0.764

TF_Lading_Grp Q vs A 1.000 0.321 0.084 1.230

TF_Lading_Grp T vs A 1.000 0.094 0.006 1.600
RA-19-01 

February 2019 

C-33 

Estimated Correlation Matrix 

Parameter Intercept SMS515 SMS516 STS JKT1 SID TFT1 ACCTYP1 SEV2 TSP

Intercept 1.0000 -0.5739 -0.4458 -0.4950 -0.2591 -0.8903 0.4340 -0.0469 0.0068 -0.0295

SMS515 -0.5739 1.0000 0.8032 0.0317 -0.1052 0.5937 0.1653 0.0184 0.0032 0.0213

SMS516 -0.4458 0.8032 1.0000 -0.0027 -0.2012 0.4690 0.2078 0.0195 0.0081 0.0040

STS -0.4950 0.0317 -0.0027 1.0000 0.0825 0.0715 -0.7664 -0.0097 0.0394 0.0085

JKT1 -0.2591 -0.1052 -0.2012 0.0825 1.0000 0.2451 -0.3062 -0.0329 0.0225 0.0462

SID -0.8903 0.5937 0.4690 0.0715 0.2451 1.0000 -0.1605 0.0044 -0.0283 -0.0041

TFT1 0.4340 0.1653 0.2078 -0.7664 -0.3062 -0.1605 1.0000 0.0180 -0.0540 -0.0438

ACCTYP1 -0.0469 0.0184 0.0195 -0.0097 -0.0329 0.0044 0.0180 1.0000 -0.0508 -0.0830

SEV2 0.0068 0.0032 0.0081 0.0394 0.0225 -0.0283 -0.0540 -0.0508 1.0000 0.0225

TSP -0.0295 0.0213 0.0040 0.0085 0.0462 -0.0041 -0.0438 -0.0830 0.0225 1.0000

TSPCDR -0.0038 0.0316 0.0373 -0.0157 -0.0600 0.0345 0.0861 0.0840 -0.0585 -0.7215

TSP2 0.0104 -0.0404 -0.0280 -0.0292 -0.0241 0.0219 0.0493 -0.0322 -0.2147 -0.8850
RA-19-01 

February 2019 

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Estimated Correlation Matrix 

Parameter Intercept SMS515 SMS516 STS JKT1 SID TFT1 ACCTYP1 SEV2 TSP

CDRTSP2 -0.0049 -0.0153 -0.0118 0.0255 0.0414 -0.0312 -0.0866 -0.0939 0.0445 0.7638

Haz_Env -0.0429 -0.0277 -0.0324 0.0100 0.0456 0.0108 -0.0389 -0.4782 0.0689 -0.1610

TSP2Haz_Env 0.0183 0.0604 0.0376 0.0230 -0.0010 -0.0109 -0.0057 0.2932 0.1670 0.2044

TF_Lading_GrpB 0.3478 -0.2178 -0.1656 -0.0209 -0.1124 -0.4602 0.2854 -0.0036 -0.0351 -0.0736

TF_Lading_GrpD 0.0691 0.1122 0.0176 -0.6945 0.1974 0.2313 0.5822 0.0258 -0.0423 -0.0457

TF_Lading_GrpE 0.3273 -0.1134 -0.1138 -0.0118 -0.0267 -0.4589 0.3065 -0.0136 -0.0402 -0.0757

TF_Lading_GrpF 0.0993 -0.0510 -0.0127 -0.0266 -0.2977 -0.1598 0.2860 0.0139 -0.0580 -0.0710

TF_Lading_GrpG -0.1257 0.0877 0.0954 0.0104 -0.1161 0.1144 0.1133 0.0023 -0.0522 -0.0330

TF_Lading_GrpH 0.2062 -0.1160 -0.0690 -0.0154 -0.1830 -0.2635 0.1767 0.0047 -0.0523 -0.0294

TF_Lading_GrpK 0.2008 -0.1231 -0.0773 -0.0199 -0.1931 -0.2529 0.1672 0.0036 -0.0451 0.0063

TF_Lading_GrpM 0.1077 -0.0400 -0.1047 -0.0129 -0.1080 -0.1386 0.1105 -0.0088 0.0090 0.0027

TF_Lading_GrpO -0.0879 0.0614 0.0708 0.0086 -0.0846 0.0764 0.0828 -0.0107 -0.0205 -0.0184

TF_Lading_GrpQ 0.0879 -0.0898 -0.0704 -0.0008 0.0033 -0.1222 0.0674 0.0025 0.0017 -0.0217

TF_Lading_GrpT 0.0443 -0.0342 -0.0286 -0.0008 -0.0309 -0.0624 0.0405 0.0167 -0.0101 -0.0155

Estimated Correlation Matrix 

Parameter TSPCDR TSP2 CDRTSP2 Haz_Env TSP2Haz_Env TF_Lading_GrpB TF_Lading_GrpD

Intercept -0.0038 0.0104 -0.0049 -0.0429 0.0183 0.3478 0.0691

SMS515 0.0316 -0.0404 -0.0153 -0.0277 0.0604 -0.2178 0.1122

SMS516 0.0373 -0.0280 -0.0118 -0.0324 0.0376 -0.1656 0.0176

STS -0.0157 -0.0292 0.0255 0.0100 0.0230 -0.0209 -0.6945

JKT1 -0.0600 -0.0241 0.0414 0.0456 -0.0010 -0.1124 0.1974

SID 0.0345 0.0219 -0.0312 0.0108 -0.0109 -0.4602 0.2313

TFT1 0.0861 0.0493 -0.0866 -0.0389 -0.0057 0.2854 0.5822

ACCTYP1 0.0840 -0.0322 -0.0939 -0.4782 0.2932 -0.0036 0.0258

SEV2 -0.0585 -0.2147 0.0445 0.0689 0.1670 -0.0351 -0.0423

TSP -0.7215 -0.8850 0.7638 -0.1610 0.2044 -0.0736 -0.0457

TSPCDR 1.0000 0.5827 -0.9464 -0.0920 -0.0305 0.0841 0.0427

TSP2 0.5827 1.0000 -0.6733 0.3313 -0.5356 0.0629 0.0686

CDRTSP2 -0.9464 -0.6733 1.0000 0.0854 -0.0005 -0.0800 -0.0701

Haz_Env -0.0920 0.3313 0.0854 1.0000 -0.6837 -0.0164 -0.0355

TSP2Haz_Env -0.0305 -0.5356 -0.0005 -0.6837 1.0000 -0.0230 -0.0075

TF_Lading_GrpB 0.0841 0.0629 -0.0800 -0.0164 -0.0230 1.0000 0.2020
RA-19-01 

February 2019 

C-35 

Estimated Correlation Matrix 

Parameter TSPCDR TSP2 CDRTSP2 Haz_Env TSP2Haz_Env TF_Lading_GrpB TF_Lading_GrpD

TF_Lading_GrpD 0.0427 0.0686 -0.0701 -0.0355 -0.0075 0.2020 1.0000

TF_Lading_GrpE 0.1014 0.0639 -0.0949 -0.0091 -0.0120 0.7669 0.2341

TF_Lading_GrpF 0.1218 0.0900 -0.1149 -0.0033 -0.0643 0.5652 0.2269

TF_Lading_GrpG 0.0161 0.0348 -0.0175 -0.0143 -0.0038 0.2154 0.1635

TF_Lading_GrpH 0.0332 0.0240 -0.0383 -0.0134 0.0089 0.3889 0.0770

TF_Lading_GrpK 0.0161 0.0038 -0.0159 -0.0222 -0.0021 0.3585 0.0661

TF_Lading_GrpM 0.0253 0.0008 -0.0405 -0.0477 0.0265 0.2583 0.0962

TF_Lading_GrpO 0.0452 0.0142 -0.0360 0.0057 -0.0018 0.1560 0.1095

TF_Lading_GrpQ 0.0191 0.0216 -0.0212 -0.0006 -0.0028 0.2158 0.0714

TF_Lading_GrpT 0.0189 0.0112 -0.0143 0.0047 -0.0035 0.1053 0.0269

Estimated Correlation Matrix 

Parameter TF_Lading_GrpE TF_Lading_GrpF TF_Lading_GrpG TF_Lading_GrpH TF_Lading_GrpK

Intercept 0.3273 0.0993 -0.1257 0.2062 0.2008

SMS515 -0.1134 -0.0510 0.0877 -0.1160 -0.1231

SMS516 -0.1138 -0.0127 0.0954 -0.0690 -0.0773

STS -0.0118 -0.0266 0.0104 -0.0154 -0.0199

JKT1 -0.0267 -0.2977 -0.1161 -0.1830 -0.1931

SID -0.4589 -0.1598 0.1144 -0.2635 -0.2529

TFT1 0.3065 0.2860 0.1133 0.1767 0.1672

ACCTYP1 -0.0136 0.0139 0.0023 0.0047 0.0036

SEV2 -0.0402 -0.0580 -0.0522 -0.0523 -0.0451

TSP -0.0757 -0.0710 -0.0330 -0.0294 0.0063

TSPCDR 0.1014 0.1218 0.0161 0.0332 0.0161

TSP2 0.0639 0.0900 0.0348 0.0240 0.0038

CDRTSP2 -0.0949 -0.1149 -0.0175 -0.0383 -0.0159

Haz_Env -0.0091 -0.0033 -0.0143 -0.0134 -0.0222

TSP2Haz_Env -0.0120 -0.0643 -0.0038 0.0089 -0.0021

TF_Lading_GrpB 0.7669 0.5652 0.2154 0.3889 0.3585

TF_Lading_GrpD 0.2341 0.2269 0.1635 0.0770 0.0661

TF_Lading_GrpE 1.0000 0.5633 0.2109 0.3926 0.3575

TF_Lading_GrpF 0.5633 1.0000 0.2793 0.3305 0.3147
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February 2019 

C-36 

Estimated Correlation Matrix 

Parameter TF_Lading_GrpE TF_Lading_GrpF TF_Lading_GrpG TF_Lading_GrpH TF_Lading_GrpK

TF_Lading_GrpG 0.2109 0.2793 1.0000 0.1304 0.1208

TF_Lading_GrpH 0.3926 0.3305 0.1304 1.0000 0.2115

TF_Lading_GrpK 0.3575 0.3147 0.1208 0.2115 1.0000

TF_Lading_GrpM 0.2695 0.2320 0.0950 0.1458 0.1387

TF_Lading_GrpO 0.1548 0.2033 0.1261 0.0935 0.0881

TF_Lading_GrpQ 0.2257 0.1671 0.0662 0.1109 0.1037

TF_Lading_GrpT 0.1082 0.0895 0.0354 0.0584 0.0547

Estimated Correlation Matrix 

Parameter TF_Lading_GrpM TF_Lading_GrpO TF_Lading_GrpQ TF_Lading_GrpT

Intercept 0.1077 -0.0879 0.0879 0.0443

SMS515 -0.0400 0.0614 -0.0898 -0.0342

SMS516 -0.1047 0.0708 -0.0704 -0.0286

STS -0.0129 0.0086 -0.0008 -0.0008

JKT1 -0.1080 -0.0846 0.0033 -0.0309

SID -0.1386 0.0764 -0.1222 -0.0624

TFT1 0.1105 0.0828 0.0674 0.0405

ACCTYP1 -0.0088 -0.0107 0.0025 0.0167

SEV2 0.0090 -0.0205 0.0017 -0.0101

TSP 0.0027 -0.0184 -0.0217 -0.0155

TSPCDR 0.0253 0.0452 0.0191 0.0189

TSP2 0.0008 0.0142 0.0216 0.0112

CDRTSP2 -0.0405 -0.0360 -0.0212 -0.0143

Haz_Env -0.0477 0.0057 -0.0006 0.0047

TSP2Haz_Env 0.0265 -0.0018 -0.0028 -0.0035

TF_Lading_GrpB 0.2583 0.1560 0.2158 0.1053

TF_Lading_GrpD 0.0962 0.1095 0.0714 0.0269

TF_Lading_GrpE 0.2695 0.1548 0.2257 0.1082

TF_Lading_GrpF 0.2320 0.2033 0.1671 0.0895

TF_Lading_GrpG 0.0950 0.1261 0.0662 0.0354

TF_Lading_GrpH 0.1458 0.0935 0.1109 0.0584
RA-19-01 

February 2019 

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Estimated Correlation Matrix 

Parameter TF_Lading_GrpM TF_Lading_GrpO TF_Lading_GrpQ TF_Lading_GrpT

TF_Lading_GrpK 0.1387 0.0881 0.1037 0.0547

TF_Lading_GrpM 1.0000 0.0674 0.0743 0.0380

TF_Lading_GrpO 0.0674 1.0000 0.0484 0.0265

TF_Lading_GrpQ 0.0743 0.0484 1.0000 0.0317

TF_Lading_GrpT 0.0380 0.0265 0.0317 1.0000

Partition for the Hosmer and Lemeshow Test 

Group Total 

TF_Loss = 1 TF_Loss = 0 

Observed Expected Observed Expected

1 448 6 3.85 442 444.15

2 447 4 6.81 443 440.19

3 451 9 8.95 442 442.05

4 447 11 11.87 436 435.13

5 447 19 22.06 428 424.94

6 447 40 47.45 407 399.55

7 447 76 70.64 371 376.36

8 447 88 92.26 359 354.74

9 447 111 112.62 336 334.38

10 439 157 153.09 282 285.91

Hosmer and Lemeshow 

Goodness-of-Fit Test 

Chi-Square DF Pr > ChiSq 

5.1212 8 0.7445 
RA-19-01 

February 2019 

C-38 

Classification Table 

Prob 

Level 

Correct Incorrect Percentages 

Event 

NonEvent Event NonEvent Correct SensitivitySpecificityFalse

POS

False

NEG

0.000 521 0 3946 0 11.7 100.0 0.0 88.3 .

0.020 503 1136 2810 18 36.7 96.5 28.8 84.8 1.6

0.040 485 1901 2045 36 53.4 93.1 48.2 80.8 1.9

0.060 476 2085 1861 45 57.3 91.4 52.8 79.6 2.1

0.080 467 2215 1731 54 60.0 89.6 56.1 78.8 2.4

0.100 453 2318 1628 68 62.0 86.9 58.7 78.2 2.8

0.120 436 2501 1445 85 65.7 83.7 63.4 76.8 3.3

0.140 416 2640 1306 105 68.4 79.8 66.9 75.8 3.8

0.160 383 2769 1177 138 70.6 73.5 70.2 75.4 4.7

0.180 351 2954 992 170 74.0 67.4 74.9 73.9 5.4

0.200 315 3103 843 206 76.5 60.5 78.6 72.8 6.2

0.220 278 3236 710 243 78.7 53.4 82.0 71.9 7.0

0.240 231 3387 559 290 81.0 44.3 85.8 70.8 7.9

0.260 175 3550 396 346 83.4 33.6 90.0 69.4 8.9

0.280 145 3660 286 376 85.2 27.8 92.8 66.4 9.3

0.300 102 3741 205 419 86.0 19.6 94.8 66.8 10.1

0.320 87 3793 153 434 86.9 16.7 96.1 63.8 10.3

0.340 82 3823 123 439 87.4 15.7 96.9 60.0 10.3

0.360 64 3843 103 457 87.5 12.3 97.4 61.7 10.6

0.380 52 3871 75 469 87.8 10.0 98.1 59.1 10.8

0.400 39 3891 55 482 88.0 7.5 98.6 58.5 11.0

0.420 29 3912 34 492 88.2 5.6 99.1 54.0 11.2

0.440 12 3924 22 509 88.1 2.3 99.4 64.7 11.5

0.460 10 3932 14 511 88.2 1.9 99.6 58.3 11.5

0.480 9 3933 13 512 88.2 1.7 99.7 59.1 11.5

0.500 5 3937 9 516 88.2 1.0 99.8 64.3 11.6

0.520 4 3941 5 517 88.3 0.8 99.9 55.6 11.6

0.540 2 3941 5 519 88.3 0.4 99.9 71.4 11.6

0.560 1 3943 3 520 88.3 0.2 99.9 75.0 11.7
RA-19-01 

February 2019 

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Classification Table 

Prob 

Level 

Correct Incorrect Percentages 

Event 

NonEvent Event NonEvent Correct SensitivitySpecificityFalse

POS

False

NEG

0.580 1 3944 2 520 88.3 0.2 99.9 66.7 11.6

0.600 1 3945 1 520 88.3 0.2 100.0 50.0 11.6

0.620 1 3945 1 520 88.3 0.2 100.0 50.0 11.6

0.640 1 3945 1 520 88.3 0.2 100.0 50.0 11.6

0.660 1 3945 1 520 88.3 0.2 100.0 50.0 11.6

0.680 1 3946 0 520 88.4 0.2 100.0 0.0 11.6

0.700 0 3946 0 521 88.3 0.0 100.0 . 11.7
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Bottom Fittings 

Model Information 

Data Set WORK.BFCPR2 

Response Variable BF_Loss 

Number of Response Levels 2 

Model binary logit 

Optimization Technique Fisher's scoring 

Likelihood Penalty Firth's bias 

correction 

Number of Observations Read 5484 

Number of Observations Used 5484 

Response Profile 

Ordered 

Value BF_Loss 

Total 

Frequency 

1 0 5344 

2 1 140 

Probability modeled is BF_Loss='1'.

Class Level Information 

Class Value 

Design 

Variables 

BF_Lading_Grp A 0 0 0 0 0 0 

D 1 0 0 0 0 0 

E 0 1 0 0 0 0 

F 0 0 1 0 0 0 

J 0 0 0 1 0 0 

K 0 0 0 0 1 0 

N 0 0 0 0 0 1 
RA-19-01 

February 2019 

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Intercept-Only Model Convergence Status 

Convergence criterion (GCONV=1E-8) 

satisfied. 

Model Convergence Status 

Convergence criterion (GCONV=1E-8) 

satisfied. 

Model Fit Statistics 

Criterion 

Intercept 

Only 

Intercept 

and 

Covariates 

AIC 1208.387 1053.618 

SC 1214.996 1159.372 

-2 Log L 1206.387 1021.618 

Testing Global Null Hypothesis: BETA=0 

Test Chi-Square DF Pr > ChiSq

Likelihood Ratio 184.7683 15 <.0001

Score 204.9466 15 <.0001

Wald 164.4706 15 <.0001

Type 3 Analysis of Effects 

Effect DF 

Wald 

Chi-Square Pr > ChiSq

JKT 1 14.3077 0.0002

STS 1 0.5032 0.4781

TSP 1 0.0156 0.9006

TSP2 1 2.5579 0.1097

SEV 1 1.6980 0.1926

CDR 1 9.0908 0.0026

Haz_Env 1 5.7701 0.0163

TSP2*CDR 1 8.1470 0.0043
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Type 3 Analysis of Effects 

Effect DF 

Wald 

Chi-Square Pr > ChiSq

SEV*Haz_Env 1 8.0248 0.0046

BF_Lading_Grp 6 56.9025 <.0001

Analysis of Maximum Likelihood Estimates 

Parameter DF Estimate 

Standard 

Error 

Wald

Chi-Square Pr > ChiSq

Intercept 1 -2.3275 3.2833 0.5025 0.4784

JKT 1 -0.8730 0.2308 14.3077 0.0002

STS 1 -5.2546 7.4073 0.5032 0.4781

TSP 1 0.00328 0.0263 0.0156 0.9006

TSP2 1 0.000846 0.000529 2.5579 0.1097

SEV 1 -0.0275 0.0211 1.6980 0.1926

CDR 1 0.0578 0.0192 9.0908 0.0026

Haz_Env 1 -0.2307 0.0960 5.7701 0.0163

TSP2*CDR 1 -0.00003 0.000010 8.1470 0.0043

SEV*Haz_Env 1 0.0111 0.00392 8.0248 0.0046

BF_Lading_Grp D 1 0.3864 1.1245 0.1181 0.7311

BF_Lading_Grp E 1 1.7277 0.2664 42.0498 <.0001

BF_Lading_Grp F 1 1.7051 0.3310 26.5384 <.0001

BF_Lading_Grp J 1 2.7727 0.9190 9.1030 0.0026

BF_Lading_Grp K 1 1.5623 0.4157 14.1269 0.0002

BF_Lading_Grp N 1 0.9318 0.3887 5.7454 0.0165

Association of Predicted Probabilities and 

Observed Responses 

Percent Concordant 81.0 Somers' D 0.622 

Percent Discordant 18.8 Gamma 0.624 

Percent Tied 0.2 Tau-a 0.031 

Pairs 748160 c 0.811 
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Odds Ratio Estimates and Wald Confidence Intervals 

Label Estimate 95% Confidence Limits 

TSP2 at 

CDR=14.267 

1.000 1.000 1.001

SEV at 

Haz_Env=4.4743 

1.022 0.997 1.049

Haz_Env at 

SEV=12.387 

0.911 0.805 1.031

CDR at 

TSP2=712.95 

1.037 1.010 1.065
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C-48 

Parameter Estimates and Wald Confidence Intervals 

Parameter Estimate 95% Confidence Limits 

Intercept -2.3275 -8.7626 4.1076

JKT -0.8730 -1.3254 -0.4207

STS -5.2546 -19.7726 9.2634

TSP 0.00328 -0.0482 0.0548

TSP2 0.000846 -0.00019 0.00188

SEV -0.0275 -0.0690 0.0139

CDR 0.0578 0.0202 0.0954

Haz_Env -0.2307 -0.4190 -0.0425

TSP2*CDR -0.00003 -0.00005 -9.35E-6

SEV*Haz_Env 0.0111 0.00342 0.0188

BF_Lading_Grp D 0.3864 -1.8175 2.5904

BF_Lading_Grp E 1.7277 1.2055 2.2499

BF_Lading_Grp F 1.7051 1.0564 2.3538

BF_Lading_Grp J 2.7727 0.9715 4.5739

BF_Lading_Grp K 1.5623 0.7476 2.3770

BF_Lading_Grp N 0.9318 0.1699 1.6937

Odds Ratio Estimates and Wald Confidence Intervals 

Effect Unit Estimate 95% Confidence Limits 

JKT 1.000 0.418 0.266 0.657

STS 1.000 0.005 <0.001 >999.999

TSP 1.000 1.003 0.953 1.056

BF_Lading_Grp D vs A 1.000 1.472 0.162 13.335

BF_Lading_Grp E vs A 1.000 5.628 3.338 9.487

BF_Lading_Grp F vs A 1.000 5.502 2.876 10.525

BF_Lading_Grp J vs A 1.000 16.001 2.642 96.917

BF_Lading_Grp K vs A 1.000 4.770 2.112 10.772

BF_Lading_Grp N vs A 1.000 2.539 1.185 5.440
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Estimated Correlation Matrix 

Parameter Intercept JKT STS TSP TSP2 SEV CDR Haz_Env TSP2CDR

Intercept 1.0000 -0.1025 -0.9896 -0.0331 0.0547 -0.0856 0.0454 -0.0952 -0.0613

JKT -0.1025 1.0000 0.0563 0.0054 -0.0365 0.0267 -0.0924 0.0289 0.0968

STS -0.9896 0.0563 1.0000 -0.0009 -0.0233 0.0203 -0.0383 0.0157 0.0475

TSP -0.0331 0.0054 -0.0009 1.0000 -0.8785 -0.1803 -0.4684 -0.2672 0.4433

TSP2 0.0547 -0.0365 -0.0233 -0.8785 1.0000 -0.0886 0.6452 0.0872 -0.7409

SEV -0.0856 0.0267 0.0203 -0.1803 -0.0886 1.0000 -0.2408 0.6827 0.2978

CDR 0.0454 -0.0924 -0.0383 -0.4684 0.6452 -0.2408 1.0000 -0.2158 -0.8308

Haz_Env -0.0952 0.0289 0.0157 -0.2672 0.0872 0.6827 -0.2158 1.0000 0.2194

TSP2CDR -0.0613 0.0968 0.0475 0.4433 -0.7409 0.2978 -0.8308 0.2194 1.0000

SEVHaz_Env 0.0786 -0.0172 -0.0103 0.2090 -0.0833 -0.7890 0.1171 -0.8150 -0.2098

BF_Lading_GrpD 0.8309 0.0822 -0.8565 0.0034 0.0148 -0.0057 -0.0012 -0.0120 -0.0239

BF_Lading_GrpE -0.0604 0.4235 -0.0143 0.0156 -0.0283 0.0138 -0.0053 0.0081 0.0371

BF_Lading_GrpF -0.0016 -0.2183 -0.0363 0.0370 -0.0080 0.0200 0.0561 -0.0171 -0.0485

BF_Lading_GrpJ -0.0223 -0.0382 0.0011 0.0457 -0.0503 -0.0108 -0.0070 0.0242 0.0290

BF_Lading_GrpK -0.0238 -0.1632 -0.0062 0.0931 -0.0745 -0.0103 -0.0704 -0.0036 0.0561

BF_Lading_GrpN -0.0657 0.2186 0.0191 0.0204 -0.0626 0.0541 -0.0841 0.0286 0.0827

Estimated Correlation Matrix 

Parameter SEVHaz_Env BF_Lading_GrpD BF_Lading_GrpE BF_Lading_GrpF 

Intercept 0.0786 0.8309 -0.0604 -0.0016 

JKT -0.0172 0.0822 0.4235 -0.2183 

STS -0.0103 -0.8565 -0.0143 -0.0363 

TSP 0.2090 0.0034 0.0156 0.0370 

TSP2 -0.0833 0.0148 -0.0283 -0.0080 

SEV -0.7890 -0.0057 0.0138 0.0200 

CDR 0.1171 -0.0012 -0.0053 0.0561 

Haz_Env -0.8150 -0.0120 0.0081 -0.0171 

TSP2CDR -0.2098 -0.0239 0.0371 -0.0485 

SEVHaz_Env 1.0000 0.0049 -0.0030 -0.0164 

BF_Lading_GrpD 0.0049 1.0000 0.2121 0.1202 

BF_Lading_GrpE -0.0030 0.2121 1.0000 0.4110 

BF_Lading_GrpF -0.0164 0.1202 0.4110 1.0000 
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Estimated Correlation Matrix 

Parameter SEVHaz_Env BF_Lading_GrpD BF_Lading_GrpE BF_Lading_GrpF 

BF_Lading_GrpJ 0.0233 0.0337 0.1694 0.1542 

BF_Lading_GrpK 0.0096 0.0792 0.3282 0.3572 

BF_Lading_GrpN 0.0027 0.1135 0.5169 0.2916 

Estimated Correlation Matrix 

Parameter BF_Lading_GrpJ BF_Lading_GrpK BF_Lading_GrpN

Intercept -0.0223 -0.0238 -0.0657

JKT -0.0382 -0.1632 0.2186

STS 0.0011 -0.0062 0.0191

TSP 0.0457 0.0931 0.0204

TSP2 -0.0503 -0.0745 -0.0626

SEV -0.0108 -0.0103 0.0541

CDR -0.0070 -0.0704 -0.0841

Haz_Env 0.0242 -0.0036 0.0286

TSP2CDR 0.0290 0.0561 0.0827

SEVHaz_Env 0.0233 0.0096 0.0027

BF_Lading_GrpD 0.0337 0.0792 0.1135

BF_Lading_GrpE 0.1694 0.3282 0.5169

BF_Lading_GrpF 0.1542 0.3572 0.2916

BF_Lading_GrpJ 1.0000 0.1286 0.1201

BF_Lading_GrpK 0.1286 1.0000 0.2403

BF_Lading_GrpN 0.1201 0.2403 1.0000

Partition for the Hosmer and Lemeshow Test 

Group Total 

BF_Loss = 1 BF_Loss = 0 

Observed Expected Observed Expected

1 548 1 1.53 547 546.47

2 212 2 0.94 210 211.06

3 1056 1 5.58 1055 1050.42

4 548 6 4.32 542 543.68

5 548 5 7.12 543 540.88

6 549 11 9.82 538 539.18
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Partition for the Hosmer and Lemeshow Test 

Group Total 

BF_Loss = 1 BF_Loss = 0 

Observed Expected Observed Expected

7 548 10 14.40 538 533.60

8 548 21 18.63 527 529.37

9 548 31 33.81 517 514.19

10 379 52 50.66 327 328.34

Hosmer and Lemeshow 

Goodness-of-Fit Test 

Chi-Square DF Pr > ChiSq 

8.5866 8 0.3784 

Classification Table 

Prob 

Level 

Correct Incorrect Percentages 

Event 

NonEvent Event NonEvent Correct SensitivitySpecificityFalse

POS

False

NEG

0.000 140 0 5344 0 2.6 100.0 0.0 97.4 .

0.020 112 3321 2023 28 62.6 80.0 62.1 94.8 0.8

0.040 83 4399 945 57 81.7 59.3 82.3 91.9 1.3

0.060 63 4672 672 77 86.3 45.0 87.4 91.4 1.6

0.080 39 5034 310 101 92.5 27.9 94.2 88.8 2.0

0.100 31 5135 209 109 94.2 22.1 96.1 87.1 2.1

0.120 26 5189 155 114 95.1 18.6 97.1 85.6 2.1

0.140 17 5224 120 123 95.6 12.1 97.8 87.6 2.3

0.160 12 5260 84 128 96.1 8.6 98.4 87.5 2.4

0.180 8 5287 57 132 96.6 5.7 98.9 87.7 2.4

0.200 8 5303 41 132 96.8 5.7 99.2 83.7 2.4

0.220 6 5311 33 134 97.0 4.3 99.4 84.6 2.5

0.240 2 5321 23 138 97.1 1.4 99.6 92.0 2.5

0.260 2 5332 12 138 97.3 1.4 99.8 85.7 2.5

0.280 2 5334 10 138 97.3 1.4 99.8 83.3 2.5

0.300 1 5337 7 139 97.3 0.7 99.9 87.5 2.5

0.320 0 5337 7 140 97.3 0.0 99.9 100 2.6
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Classification Table 

Prob 

Level 

Correct Incorrect Percentages 

Event 

NonEvent Event NonEvent Correct SensitivitySpecificityFalse

POS

False

NEG

0.340 0 5341 3 140 97.4 0.0 99.9 100 2.6

0.360 0 5343 1 140 97.4 0.0 100.0 100 2.6

0.380 0 5344 0 140 97.4 0.0 100.0 . 2.6
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Appendix D 

Uncertainty Surrounding CPR 

All estimates/predictions in the study are accompanied by uncertainty. The methods and 

the final models were chosen to limit and, to the extent possible, minimize this 

uncertainty, but it cannot be eliminated. 

To assist in placing the appropriate weight on the estimates for decision-making 

purposes, it can be worthwhile to examine a confidence interval around key CPRs. 

A large-sample 95% confidence interval for s prediction is given by 

 (15) 

This transforms to a confidence interval for P of 

 

 (16) 

When comparing two CPRs, if one falls within the confidence interval around the other, 

then the two estimates are not statistically distinct, i.e., there is no evidence that the true 

CPRs for those two cars are actually different. 

Table 12 provides examples. 

 
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D-2 

Table 12 

CPR Estimates and Associated Confidence Intervals for Five Tank Car Configurations 

Car Estimated 

Mainline 

CPR 

Lower 95% 

Confidence 

Bound 

Higher 95% 

Confidence 

Bound 

1 111A100W1, 7/16” tank, no jacket, 

bottom fittings, 119” ID 

0.274 0.239 0.293 

2 111A100W1, 7/16” tank, jacket, bottom 

fittings, 119” ID 

0.134 0.119 0.151 

3 CPC-1232, 1/2” tank, no jacket, halfheight head shield, top fittings protection, 

bottom fittings, 119” ID 

0.132 0.117 0.148 

4 CPC-1232, 7/16” tank, jacket, full head 

shield, top fittings protection, bottom 

fittings, 119” ID 

0.064 0.054 0.074 

5 DOT-117, 9/16” tank, jacket, full head 

shield, top fittings protection, bottom 

fittings, 119” ID 

0.042 0.034 0.050 

Figure 9 shows the same data, and makes clear that cars 2 and 3, for which the CPRs fall within 

each other’s confidence intervals, are not statistically significantly different in CPR, but the CPR 

differences between all other pairings are statistically significant. 

Figure 9 

CPRs for Five Tank Cars, with 95% Confidence Intervals 
RA-19-01 

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E-1 

Appendix E 

Calculation of the FRA Accident Data Compatibility Multiplier 

Tank cars are entered in TCAD when they experience damage to tank-car-specific features in an 

accident. Therefore, if the fraction (cars releasing lading)/(cars in the database) is calculated, 

this results in an estimate of the probability of lading loss, conditional on being in the database, 

i.e., being damaged. 

However, such an estimate is not particularly useful in a broader risk assessment or cost-benefit 

analysis. It cannot be connected to accident rate data, for example. If the denominator can be 

converted into the number of tank cars derailed in FRA-reportable accidents, on the other hand, 

then the resulting probability estimate can be combined with published FRA accident rates. 

Such a conversion would account for tank cars that are derailed in reportable accidents, but not 

damaged on the tank, jacket, fittings, or head shield. Also, tank cars that are in TCAD but 

derailed in accidents that did not meet the FRA cost threshold for reporting would also be 

accounted for. 

Two approaches to estimating the adjustment, which takes the form of a multiplicative factor 

referred to as the FRA multiplier, are explored below. 

The first approach uses a sample of data from Burlington Northern Santa Fe Railway (BNSF) 

covering the period 2000-2010. In this dataset, it was known that each record corresponded to an 

FRA-reportable accident, and that these were all of the tank cars derailed in FRA-reportable 

accidents on the BNSF system in that period. All data were for mainline accidents. These data 

were compared to data in TCAD that were associated with accidents on BNSF. 

The maximum likelihood estimator (MLE) of the ratio between BNSF/FRA and TCAD loss 

probability estimates is calculated using equation (17): 

^ FRA FRA

SP SP

CPR L /N = = CPR L /N

FRA

SP

M (17)

where: 

^

M = estimated FRA multiplier 

LFRA = number of tank cars with lading loss in FRA-reportable accidents, 

NFRA = number of tank cars derailed in the FRA-reportable accidents. 

LSP = number of tank cars with lading loss in the TCAD data, and 

NSP = number of tank cars in the TCAD data 

The (100-α)% large sample asymptotic confidence interval of estimated multiplier can be 

expressed as: 
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E-2 

 ^

1 /2 exp(ln ) M  z SE a (18)

where 

 FRA FRA SP SP

1 1 11

L N LN SE   (19) 

Data for the BNSF mainline accidents in 2000-2010 were as follows: 

 BNSF Records 

Known to Be 

FRA-Reportable 

All TCAD 

BNSF Records 

Cars with loss, L 115 66 

Cars in dataset, N 470 355 

CPR, L/N 0.245 0.186 

The estimated FRA multiplier for mainlines arising from this procedure is 

^ FRA FRA

SP SP

CPR L /N = = CPR L /N

FRA

SP

M =1.32 (20) 

with a corresponding 95% confidence interval is (1.01, 1.72). The 99% confidence interval is 

(0.92, 1.88). Note that the value of one falls within the 99% interval, but not the 95% interval. 

The P-value for a test of difference from one is 0.046. Whether there is statistically significant 

evidence that the mainline multiplier is different from one is dependent on the analyst’s selection 

of significance level. At 5% significance level, the multiplier appears to be greater than one. At 

1% significance level, no difference is found. 

It was decided to consider this analysis as insufficient evidence of a multiplier different from 

one, for the following reasons: 

1) The p-value is borderline, 

2) The form of the confidence interval is defensible for sufficiently large sample sizes, and 

incurs some uncertainty at moderate sample sizes, 

3) It is unclear how representative BNSF data for the whole rail industry, and 

4) The observations are not, strictly speaking, independent, since some come from the same 

accident. 

A second approach was to attempt to assign a FRA-reportable status to a larger group of cars in 

TCAD for 2000-2010. Some railroads indirectly inform the Tank Car Safety Project when an 

accident was reported to FRA by using the same report submission number for their FRA report 

and for information provided to the Project. Tank cars identified this way, damaged in mainline 

accidents, broke down as follows: 
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February 2019 

E-3 

 TCAD Records 

Known to Be 

FRA-Reportable 

All TCAD 

Mainline 

Records for the 

Period 

Cars with loss, L 303 376 

Cars in dataset, N 1,310 1,699 

CPR, L/N 0.231 0.221 

For this dataset, 

^ FRA FRA

SP SP

CPR L /N = = CPR L /N

FRA

SP

M = 1.05. (21) 

The corresponding 95% confidence Interval is (0.91, 1.19). The confidence interval contains the 

value one. Therefore, even at 95% confidence, there is no evidence of a difference between the 

loss ratios from FRA-reportable TCAD accidents and all of TCAD for mainlines. This result 

reinforces the earlier conclusion that the mainline FRA multiplier should be set at 1. 

The previous study, RA-05-02 [Ref. 4], provided separate FRA multipliers for mainline/siding 

and yard/industrial track types. In this study the track type variable was included in the 

regressions directly, and found to be insignificant on its own. Therefore, it was deemed adequate 

to use appropriate train speeds and derailment sizes for the two different track types, and let 

those differences drive any difference in CPRs. 

It is still possible that the degree of correlation between an accident being FRA-reportable and 

that accident causing TCAD-recordable damage could differ between track types. Further work 

could be done to resolve this. Also, the magnitude of multipliers and the need for multipliers 

could change over time so the term has been kept in the model in case such a need arises. 

Note that the FRA multiplier does not have any bearing on comparisons among car 

configurations, as the percent difference between CPRs for different cars remains the same no 

matter what multiplier is used. 
RA-19-01 

February 2019 

F-1 

Appendix F 

Comparison of TWP-17 and RA-05-02 CPR Estimates 

Table 13 compares the CPR estimates derived in this study to those for the same cars using the 

RA-05-02 formulas. Note that TWP-17 CPRs are consistently lower. This could be due to a 

number of factors that cannot be verified. The distribution of accident environments has 

probably changed over time. The robustness of materials and/or designs that are lumped under 

one term in this study, such as “TC-128” or “head shield”, may have generally improved over 

time. In any event, the lower rates of release are validated by the broader data in the Tank Car 

Safety project database; note that the mainline FRA multiplier is 1.0. 

Table 13 

TWP-17 CPRs and RA-05-02 CPRs for Selected Tank Cars 

Under Average Mainline Derailment Conditions 

Car 

Specification 

Head and 

Shell 

Thickness 

(in.) 

Jacket Head 

Shield 

Top 

Fittings 

Protection 

Bottom 

Fittings 

Shell 

Inside 

Diameter 

(in.) 

TWP-17 

CPR 

RA-05-02 

CPR 

Difference 

111A100W1 0.4375 No No No Yes 119 0.274 0.353 -0.079 

111A100W1/3 0.4375 Yes No No Yes 119 0.134 0.207 -0.073 

111A100W1/2 0.4375 No No No No 119 0.265 0.310 -0.045 

111A100W1/2/3 0.4375 Yes No No No 119 0.130 0.170 -0.040 

111A100W2 0.5625 No No Yes No 100.625 0.201 0.202 -0.001 

111A100W1 0.4375 Yes Full Yes Yes 119 0.064 0.150 -0.086 

111A/S100W1 0.500 No Half Yes Yes 119 0.132 0.241 -0.109 

117R100W 0.4375 Yes Full No Yes 119 0.126 0.188 -0.062 

117R100W 0.4375 Yes Full Yes Yes 119 0.064 0.150 -0.086 

117R100W 0.500 Yes Full No Yes 119 0.106 0.176 -0.070 

117R100W 0.500 Yes Full Yes Yes 119 0.052 0.137 -0.085 

117J100W 0.5625 Yes Full Yes Yes 119 0.042 0.126 -0.084 

112J340W 0.625 Yes Full Yes No 118.75 0.033 0.076 -0.043 

105J300W 0.5625 Yes Full Yes No 118.75 0.040 0.086 -0.046 

105A500W 0.779 Yes No Yes No 102 0.040 0.073 -0.033 

105J500W 0.797 Yes Full Yes No 102 0.031 0.060 -0.029 

112J500I H1.03 / S0.89 Yes Full Yes No 115.34 0.017 0.049 -0.032 

105J600I H1.136/S0.98 Yes Full Yes No 106 0.016 0.047 -0.031